Patent Publication Number: US-6701236-B2

Title: Intelligent mechatronic control suspension system based on soft computing

Description:
BACKGROUND 
     1. Field of the Invention 
     The disclosed invention is relates generally to control systems, and more particularly to electronically controlled suspension systems. 
     2. Description of the Related Art 
     Feedback control systems are widely used to maintain the output of a dynamic system at a desired value in spite of external disturbances that would displace it from the desired value. For example, a household space-heating furnace, controlled by a thermostat, is an example of a feedback control system. The thermostat continuously measures the air temperature inside the house, and when the temperature falls below a desired minimum temperature the thermostat turns the furnace on. When the interior temperature reaches the desired minimum temperature, the thermostat turns the furnace off. The thermostat-furnace system maintains the household temperature at a substantially constant value in spite of external disturbances such as a drop in the outside temperature. Similar types of feedback controls are used in many applications. 
     A central component in a feedback control system is a controlled object, a machine, or a process that can be defined as a “plant”, having an output variable or performance characteristic to be controlled. In the above example, the “plant” is the house, the output variable is the interior air temperature in the house and the disturbance is the flow of heat (dispersion) through the walls of the house. The plant is controlled by a control system. In the above example, the control system is the thermostat in combination with the furnace. The thermostat-furnace system uses simple on-off feedback control system to maintain the temperature of the house. In many control environments, such as motor shaft position or motor speed control systems, simple on-off feedback control is insufficient. More advanced control systems rely on combinations of proportional feedback control, integral feedback control, and derivative feedback control. A feedback control based on a sum of proportional feedback, plus integral feedback, plus derivative feedback, is often referred as PID control. 
     A PID control system is a linear control system that is based on a dynamic model of the plant. In classical control systems, a linear dynamic model is obtained in the form of dynamic equations, usually ordinary differential equations. The plant is assumed to be relatively linear, time invariant, and stable. However, many real-world plants are time-varying, highly non-linear, and unstable. For example, the dynamic model may contain parameters (e.g., masses, inductance, aerodynamics coefficients, etc.), which are either only approximately known or depend on a changing environment. If the parameter variation is small and the dynamic model is stable, then the PID controller may be satisfactory. However, if the parameter variation is large or if the dynamic model is unstable, then it is common to add adaptive or intelligent (AI) control functions to the PID control system. 
     AI control systems use an optimizer, typically a non-linear optimizer, to program the operation of the PID controller and thereby improve the overall operation of the control system. 
     Classical advanced control theory is based on the assumption that near of equilibrium points all controlled “plants” can be approximated as linear systems. Unfortunately, this assumption is rarely true in the real world. Most plants are highly nonlinear, and often do not have simple control algorithms. In order to meet these needs for a nonlinear control, systems have been developed that use soft computing concepts such as genetic algorithms, fuzzy neural networks, fuzzy controllers and the like. By these techniques, the control system evolves (changes) over time to adapt itself to changes that may occur in the controlled “plant” and/or in the operating environment. 
     Currently, self-organizing control systems based on fuzzy controllers suffer from two drawbacks. First, when a genetic analyzer is used to develop a teaching signal for a fuzzy neural network, the teaching signal typically contains unnecessary stochastic noise, making it difficult to later develop an approximation to the teaching signal. Second, the fitness functions used for the genetic analyzers in self-organizing suspension control systems typically optimize the control system according to some desired control paradigm without reference to human factors such as rider comfort. 
     SUMMARY 
     The present invention solves these and other problems by providing a control system for optimizing a shock absorber system having a non-linear kinetic characteristic. The control system uses a fitness (performance) function that is based on the physical laws of minimum entropy and biologically inspired constraints relating to rider comfort, driveability, etc. In one embodiment, a genetic analyzer is used in an off-line mode to develop a teaching signal. An information filter is used to filter the teaching signal to produce a compressed teaching signal. The compressed teaching signal can be approximated online by a fuzzy controller that operates using knowledge from a knowledge base. The control system can be used to control complex plants described by nonlinear, unstable, dissipative models. The control system is configured to use smart simulation techniques for controlling the shock absorber (plant). 
     In one embodiment, the control system comprises a learning system, such as a neural network that is trained by a genetic analyzer. The genetic analyzer uses a fitness function that maximizes sensor information while minimizing entropy production based on biologically-inspired constraints. 
     In one embodiment, a suspension control system uses a difference between the time differential (derivative) of entropy (called the production entropy rate) from the learning control unit and the time differential of the entropy inside the controlled process (or a model of the controlled process) as a measure of control performance. In one embodiment, the entropy calculation is based on a thermodynamic model of an equation of motion for a controlled process plant that is treated as an open dynamic system. 
     The control system is trained by a genetic analyzer that generates a teaching signal. The optimized control system provides an optimum control signal based on data obtained from one or more sensors. For example, in a suspension system, a plurality of angle and position sensors can be used. In an off-line learning mode (e.g., in the laboratory, factory, service center, etc.), fuzzy rules are evolved using a kinetic model (or simulation) of the vehicle and its suspension system. Data from the kinetic model is provided to an entropy calculator that calculates input and output entropy production of the model. The input and output entropy productions are provided to a fitness function calculator that calculates a fitness function as a difference in entropy production rates for the genetic analyzer constrained by one or more constraints obtained from rider preferences. The genetic analyzer uses the fitness function to develop a training signal for the off-line control system. The training signal is filtered to produce a compressed training signal. Control parameters from the off-line control system are then provided to an online control system in the vehicle that, using information from a knowledge base, develops an approximation to the compressed training signal. 
     In one embodiment, the invention includes a method for controlling a nonlinear object (a plant) by obtaining an entropy production difference between a time differentiation (dS u /dt) of the entropy of the plant and a time differentiation (dS c /dt) of the entropy provided to the plant from a controller. A genetic algorithm that uses the entropy production difference as a fitness (performance) function evolves a control rule in an off-line controller. The nonlinear stability characteristics of the plant are evaluated using a Lyapunov function. The genetic analyzer minimizes entropy and maximizes sensor information content. Filtered control rules from the off-line controller are provided to an online controller to control suspension system. In one embodiment, the online controller controls the damping factor of one or more shock absorbers (dampers) in the vehicle suspension system. 
     In some embodiments, the control method also includes evolving a control rule relative to a variable of the controller by means of a genetic algorithm. The genetic algorithm uses a fitness function based on a difference between a time differentiation of the entropy of the plant (dS u /dt) and a time differentiation (dS c /dt) of the entropy provided to the plant. The variable can be corrected by using the evolved control rule. 
     In one embodiment, the invention comprises a self-organizing control system adapted to control a nonlinear plant. The AI control system includes a simulator configured to use a thermodynamic model of a nonlinear equation of motion for the plant. The thermodynamic model is based on a Lyapunov function (V), and the simulator uses the function V to analyze control for a state stability of the plant. The control system calculates an entropy production difference between a time differentiation of the entropy of said plant (dS u /dt) and a time differentiation (dS c /dt) of the entropy provided to the plant by a low-level controller that controls the plant. The entropy production difference is used by a genetic algorithm to obtain an adaptation function wherein the entropy production difference is minimized in a constrained fashion. The genetic algorithm provides a teaching signal. The teaching signal is filtered to remove stochastic noise to produce a filtered teaching signal. The filtered teaching signal is provided to a fuzzy logic classifier that determines one or more fuzzy rules by using a learning process. The fuzzy logic controller is also configured to form one or more control rules that set a control variable of the controller in the vehicle. 
     In yet another embodiment, the invention comprises a new physical measure of control quality based on minimum production entropy and using this measure for a fitness function of genetic algorithm in optimal control system design. This method provides a local entropy feedback loop in the control system. The entropy feedback loop provides for optimal control structure design by relating stability of the plant (using a Lyapunov function) and controllability of the plant (based on production entropy of the control system). The control system is applicable to a wide variety of control systems, including, for example, control systems for mechanical systems, bio-mechanical systems, robotics, electro-mechanical systems, etc. 
    
    
     BRIEF DESCRIPTION OF THE FIGURES 
     The above and other aspects, features, and advantages of the present invention will be more apparent from the following description thereof presented in connection with the following drawings. 
     FIG. 1 illustrates a general structure of a self-organizing intelligent control system based on soft computing. 
     FIG. 2 illustrates the structure of a self-organizing intelligent suspension control system with physical and biological measures of control quality based on soft computing 
     FIG. 3 illustrates the process of constructing the Knowledge Base (KB) for the Fuzzy Controller (FC). 
     FIG. 4 shows twelve typical road profiles. 
     FIG. 5 shows a normalized auto-correlation function for different velocities of motion along the road number  9  from FIG.  4 . 
     FIG. 6A is a plot showing results of stochastic simulations based on a one-dimensional Gaussian probability density function. 
     FIG. 6B is a plot showing results of stochastic simulations based on a one-dimensional uniform probability density function. 
     FIG. 6C is a plot showing results of stochastic simulations based on a one-dimensional Rayleigh probability density function. 
     FIG. 6D is a plot showing results of stochastic simulations based on a two-dimensional Gaussian probability density function. 
     FIG. 6E is a plot showing results of stochastic simulations based on a two-dimensional uniform probability density function. 
     FIG. 6F is a plot showing results of stochastic simulations based on a two-dimensional hyperbolic probability density function. 
     FIG. 7 illustrates a full car model. 
     FIG. 8A shows a control damper layout for a suspension-controlled vehicle having adjustable dampers. 
     FIG. 8B shows an adjustable damper for the suspension-controlled vehicle. 
     FIG. 8C shows fluid flow for soft and hard damping in the adjustable damper from FIG.  8 B. 
     FIG. 9 shows damper force characteristics for the adjustable dampers illustrated in FIG.  8 . 
     FIG. 10 shows the structure of an SSCQ for use in connection with a simulation model of the full car and suspension system. 
     FIG. 11 is a flowchart showing operation of the SSCQ. 
     FIG. 12 shows time intervals associated with the operating mode of the SSCQ. 
     FIG. 13 is a flowchart showing operation of the SSCQ in connection with the GA. 
     FIG. 14 shows the genetic analyzer process and the operations of reproduction, crossover, and mutation. 
     FIG. 15 shows results of variables for the fuzzy neural network. 
     FIG. 16A shows control of a four-wheeled vehicle using two controllers. 
     FIG. 16B shows control of a four-wheeled vehicle using a single controller to control all four wheels. 
     FIG. 17 shows an information filter application results for compression of a normal distribution stochastic signal, including: (a) the source signal; (b) the row-wise information distribution before compression; (c) the signal after compression; and (d) the information distribution after compression. 
     FIG. 18 shows the teaching signal K c  provided by the information filter  241  shown in FIG.  2 . 
     FIG. 19 shows the output of the simulation system of control quality of intelligent control suspension system. 
     FIG. 20 shows the simulation results of fuzzy control of a suspension system 
     FIG. 21 shows the square of heave jerk for controlled and uncontrolled systems. 
     FIG. 22 shows the square of pitch jerk for controlled and uncontrolled systems. 
     FIG. 23 shows the square of roll jerk for controlled and uncontrolled systems. 
    
    
     In the drawings, the first digit of any three-digit element reference number generally indicates the number of the figure in which the referenced element first appears. The first two digits of any four-digit element reference number generally indicate the figure in which the referenced element first appears. 
     DESCRIPTION 
     FIG. 1 is a block diagram of a control system  100  for controlling a plant based on soft computing. In the controller  100 , a reference signal y is provided to a first input of an adder  105 . An output of the adder  105  is an error signal ε, which is provided to an input of a Fuzzy Controller (FC)  143  and to an input of a Proportional-Integral-Differential (PID) controller  150 . An output of the PID controller  150  is a control signal u*, which is provided to a control input of a plant  120  and to a first input of an entropy-calculation module  132 . A disturbance m(t)  110  is also provided to an input of the plant  120 . An output of the plant  120  is a response x, which is provided to a second input the entropy-calculation module  132  and to a second input of the adder  105 . The second input of the adder  105  is negated such that the output of the adder  105  (the error signal ε) is the value of the first input minus the value of the second input. 
     An output of the entropy-calculation module  132  is provided as a fitness function to a Genetic Analyzer (GA)  131 . An output solution from the GA  131  is provided to an input of a FNN  142 . An output of the FNN  142  is provided as a knowledge base to the FC  143 . An output of the FC  143  is provided as a gain schedule to the PID controller  150 . 
     The GA  131  and the entropy calculation module  132  are part of a Simulation System of Control Quality (SSCQ)  130 . The FNN  142  and the FC  143  are part of a Fuzzy Logic Classifier System (FLCS)  140 . 
     Using a set of inputs, and the fitness function  132 , the genetic algorithm  131  works in a manner similar to a biological evolutionary process to arrive at a solution which is, hopefully, optimal. The genetic algorithm  131  generates sets of “chromosomes” (that is, possible solutions) and then sorts the chromosomes by evaluating each solution using the fitness function  132 . The fitness function  132  determines where each solution ranks on a fitness scale. Chromosomes (solutions) which are more fit are those chromosomes which correspond to solutions that rate high on the fitness scale. Chromosomes which are less fit are those chromosomes which correspond to solutions that rate low on the fitness scale. 
     Chromosomes that are more fit are kept (survive) and chromosomes that are less fit are discarded (die). New chromosomes are created to replace the discarded chromosomes. The new chromosomes are created by crossing pieces of existing chromosomes and by introducing mutations. 
     The PID controller  150  has a linear transfer function and thus is based upon a linearized equation of motion for the controlled “plant”  120 . Prior art genetic algorithms used to program PID controllers typically use simple fitness and thus do not solve the problem of poor controllability typically seen in linearization models. As is the case with most optimizers, the success or failure of the optimization often ultimately depends on the selection of the performance (fitness) function. 
     Evaluating the motion characteristics of a nonlinear plant is often difficult, in part due to the lack of a general analysis method. Conventionally, when controlling a plant with nonlinear motion characteristics, it is common to find certain equilibrium points of the plant and the motion characteristics of the plant are linearized in a vicinity near an equilibrium point. Control is then based on evaluating the pseudo (linearized) motion characteristics near the equilibrium point. This technique is scarcely, if at all, effective for plants described by models that are unstable or dissipative. 
     Computation of optimal control based on soft computing includes the GA  131  as the first step of global search for an optimal solution on a fixed space of positive solutions. The GA searches for a set of control weights for the plant. Firstly the weight vector K={k 1 , . . . , k n } is used by a conventional proportional-integral-differential (PID) controller  150  in the generation of a signal u*=δ(K) which is applied to the plant. The entropy S(δ(K)) associated to the behavior of the plant  120  on this signal is used as a fitness function by the GA  131  to produce a solution that gives minimum entropy production. The GA  131  is repeated several times at regular time intervals in order to produce a set of weight vectors K. The vectors K generated by the GA  131  are then provided to the FNN  142  and the output of the FNN  142  to the fuzzy controller  143 . The output of the fuzzy controller  143  is a collection of gain schedules for the PID controller  150  that controls the plant. For the soft computing system  100  based on a genetic analyzer, there is very often no real control law in the classical control sense, but rather, control is based on a physical control law such as minimum entropy production. 
     In order to realize an intelligent mechatronic suspension control system, the structure depicted on FIG. 1 is modified, as shown on FIG. 2 to produce a system  200  for controlling a plant, such as suspension system. The system  200  is similar to the system  100  with the addition of an information filter  241  and biologically-inspired constraints  233  in the fitness function  132 . The information filter  241  is placed between the GA  131  and the FNN  142  such that a solution vector output K i  from the GA  131  is provided to an input of the information filter  241 . An output of the information filter  241  is a filtered solution vector K c  that is provided to the input of the FNN  142 . In FIG. 2, the disturbance  110  is a road signal m(t). (e.g., measured data or data generated via stochastic simulation). In FIG. 2, the plant  120  is a suspension system and car body. The fitness function  132 , in addition to entropy production rate, includes biologically-inspired constraints based on mechanical and/or human factors. In one embodiment, the filter  241  includes an information compressor that reduces unnecessary noise in the input signal of the FNN  142 . In FIG. 2, the PID controller  150  is shown as a proportional damping force controller. 
     As shown in FIG. 3, realization of the structure depicted in FIG. 2 is divided into four development stages. The development stages include a teaching signal acquisition stage  301 , a teaching signal compression stage  302 , a teaching signal approximation stage  303 , and a knowledge base verification stage  304 . 
     The teaching signal acquisition stage  301  includes the acquisition of a robust teaching signal without the loss of information. In one embodiment, the stage  301  is realized using stochastic simulation of a full car with a Simulation System of Control Quality (SSCQ) under stochastic excitation of a road signal. The stage  301  is based on models of the road, of the car body, and of models of the suspension system. Since the desired suspension system control typically aims for the comfort of a human, it is also useful to develop a representation of human needs, and transfer these representations into the fitness function  132  as constraints  233 . 
     The output of the stage  301  is a robust teaching signal K i , which contains information regarding the car behavior and corresponding behavior of the control system. 
     Behavior of the control system is obtained from the output of the GA  131 , and behavior of the car is a response of the model for this control signal. Since the teaching signal K i  is generated by a genetic algorithm, the teaching signal K i  typically has some unnecessary stochastic noise in it. The stochastic noise can make it difficult to realize (or develop a good approximation for) the teaching signal K i . Accordingly, in a second stage  302 , the information filter  241  is applied to the teaching signal K i  to generate a compressed teaching signal K c . The information filter  241  is based on a theorem of Shannon&#39;s information theory (the theorem of compression of data). The information filter  241  reduces the content of the teaching signal by removing that portion of the teaching signal K i  that corresponds to unnecessary information. The output of the second stage  302  is a compressed teaching signal K c . 
     The third stage  303  includes approximation of the compressed teaching signal K c  by building a fuzzy inference system using a fuzzy logic classifier (FLC) based on a Fuzzy Neural Network (FNN). Information of car behavior can be used for training an input part of the FNN, and corresponding information of controller behavior can be used for output-part training of the FNN. 
     The output of the third stage  303  is a knowledge base (KB) for the FC  143  obtained in such a way that it has the knowledge of car behavior and knowledge of the corresponding controller behavior with the control quality introduced as a fitness function in the first stage  301  of development. The KB is a data file containing control laws of the parameters of the fuzzy controller, such as type of membership functions, number of inputs, outputs, rule base, etc. 
     In the fourth stage  304 , the KB can be verified in simulations and in experiments with a real car, and it is possible to check its performance by measuring parameters that have been optimized. 
     To summarize, the development of the KB for an intelligent control suspension system includes: 
     I. Obtaining a stochastic model of the road or roads. 
     II. Obtaining a realistic model of a car and its suspension system. 
     III. Development of a Simulation System of Control Quality with the car model for genetic algorithm fitness function calculation, and introduction of human needs in the fitness function. 
     IV. Development of the information compressor (information filter). 
     V. Approximation of the teaching signal with a fuzzy logic classifier system (FLCS) and obtaining the KB for the FC 
     VI. Verification of the KB in experiment and/or in simulations of the full car model with fuzzy control 
     I. Obtaining Stochastic Models of the Roads 
     It is convenient to consider different types of roads as stochastic processes with different auto-correlation functions and probability density functions. FIG. 4 shows twelve typical road profiles. Each profile shows distance along the road (on the x-axis), and altitude of the road (on the y-axis) with respect to a reference altitude. FIG. 5 shows a normalized auto-correlation function for different velocities of motion along the road number  9  (from FIG.  4 ). In FIG. 5, a curve  501  and a curve  502  show the normalized auto-correlation function for a velocity =1 meter/sec, a curve  503  shows the normalized auto-correlation function for =5 meter/sec, and a curve  504  shows the normalized auto-correlation function for =10 meter/sec. 
     The results of statistical analysis of actual roads, as shown in FIG. 4, show that it is useful to consider the road signals as stochastic processes using the following three typical auto-correlation functions. 
     
       
           R (τ)= B (0)exp{−α 1 |τ|};  (1.1) 
       
     
     
       
           R (τ)= B (0)exp{−α 1 |τ|}cos β 1 τ;  (1.2) 
       
     
     
       
         
           
             
               
                 
                   
                     
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     where α 1  and β 1  are the values of coefficients for single velocity of motion. The ranges of values of these coefficients are obtained from experimental data as: 
     α 1 =0.014 to 0.111; β 1 =0.025 to 0.140. 
     For convenience, the roads are divided into three classes: 
     A. {square root over (B(0))}≦10 sm—small obstacles; 
     B. {square root over (B(0))}=10 sm to 20 sm—medium obstacles; 
     C. {square root over (B(0))}&gt;20 sm—large obstacles. 
     The presented auto-correlation functions and its parameters are used for stochastic simulations of different types of roads using forming filters. The methodology of forming filter structure can be described according to the first type of auto-correlation functions (1.1) with different probability density functions. 
     Consider a stationary stochastic process X(t) defined on the interval [x l ,x r ], which can be either bounded or unbounded. Without loss of generality, assume that X(t) has a zero mean. Then x l &lt;0 and x r &gt;0. With the knowledge of the probability density p(x) and the spectral density Φ XX (ω) of X(t), one can establish a procedure to model the process X(t). 
     Let the spectral density be of the following low-pass type:                    Φ   XX          (   ω   )       =       α                   σ   2         π                   (       ω   2     +     α   2       )           ,     α   &gt;   0     ,           (   2.1   )                         
     where σ 2  is the mean-square value of X(t). If X(t) is also a diffusive Markov process, then it is governed by the following stochastic differential equation in the Ito sense (see Appendix I): 
     
       
           dX=−αXdt+D ( X ) dB ( t ),  (2.2) 
       
     
     where α is the same parameter in (2.1), B(t) is a unit Wiener process, and the coefficients −αX and D(X) are known as drift and the diffusion coefficients, respectively. To demonstrate that this is the case, multiply (2.2) by X(t−τ) and take the ensemble average to yield                         R        (   τ   )              τ       =       -   α                     R        (   τ   )           ,           (   2.3   )                         
     where R(τ) is the correlation function of X(t), namely, R(τ)=E[X(t−τ)X(t)]. Equation (2.3) has a solution 
     
       
           R (τ)= A exp(−α|τ|)  (2.4) 
       
     
     in which A is arbitrary. By choosing A=σ 2 , equations (2.1) and (2.4) become a Fourier transform pair. Thus equation (2.2) generates a process X(t) with a spectral density (2.1). Note that the diffusion coefficient D(X) has no influence on the spectral density. 
     Now it is useful to determine D(X) so that X(t) possesses a given stationary probability density p(x). The Fokker-Planck equation, governing the probability density p(x) of X(t) in the stationary state, is obtained from equation (2.2) as follows:                            x          G     =         -             x              {       α                   xp        (   x   )         +       1   2                    x       [         D   2          (   x   )            p        (   x   )         ]         }       =   0       ,           (   2.5   )                         
     where G is known as the probability flow. Since X(t) is defined on [x l ,x r ], G must vanish at the two boundaries x=x l  and x=x r . In the present one-dimensional case, G must vanish everywhere; consequently, equation (2.5) reduces to                  α                   xp        (   x   )         +       1   2                    x       [         D   2          (   x   )            p        (   x   )         ]         =   0.           (   2.6   )                         
     Integration of equation (2.6) results in                      D   2          (   x   )            p        (   x   )         =         -   2                   α                     ∫     x   l       x   r              up        (   u   )               u           +   C       ,           (   2.7   )                         
     where C is an integration constant. To determine the integration constant C, two cases are considered. For the first case, if x l =−∞, or x r =∞, or both, then p(x)must vanish at the infinite boundary; thus C=0 from equation (2.7). For the second case, if both x l  and x r  are finite, then the drift coefficient −αx l  at the left boundary is positive, and the drift coefficient −αx r  at the right boundary is negative, indicating that the average probability flows at the two boundaries are directed inward. However, the existence of a stationary probability density implies that all sample functions must remain within [x l ,x r ], which requires additionally that the drift coefficient vanish at the two boundaries, namely, D 2 (x l )=D 2 (x r )=0. This is satisfied only if C=0. In either case,                  D   2          (   x   )       =       -       2                 α       p        (   x   )                  ∫     x   l       x   r              up        (   u   )                 u     .                   (   2.8   )                         
     Function D 2 (x), computed from equation (2.8), is non-negative, as it should be, since p(x)≧0 and the mean value of X(t) is zero. Thus the stochastic process X(t) generated from (2.2) with D(x) given by (2.8) possesses a given stationary probability density p(x) and the spectral density (2.1). 
     The Ito type stochastic differential equation (2.2) may be converted to that of the Stratonovich type (see Appendix I) as follows:                  X   .     =         -   α                   X     -       1   4                   D   2          (   X   )              X         +         D        (   X   )           2                 π              ξ        (   t   )             ,           (   2.9   )                         
     where ξ(t) is a Gaussian white noise with a unit spectral density. Equation (2.9) is better suited for simulating sample functions. Some illustrative examples are given below. 
     EXAMPLE 1 
     Assume that X(t) is uniformly distributed, namely,                  p        (   x   )       =     1     2                 Δ         ,       -   Δ     ≤   x   ≤     Δ   .               (   2.10   )                         
     Substituting (2.10) into (2.8) 
     
       
           D   2 ( x )=α(Δ 2   −x   2 ).  (2.11) 
       
     
     In this case, the desired Ito equation is given by 
     
       
           dX=−αXdt +{square root over (α(Δ 2   −X   2 ))} dB ( t ).  (2.12) 
       
     
     It is of interest to note that a family of stochastic processes can be obtained from the following generalized version of (2.12): 
     
       
           dX=−αXdt +{square root over (αβ(Δ 2   −X   2 ))} dB ( t ).  (2.13) 
       
     
     Their appearances are strikingly diverse, yet they share the same spectral density (2.1). 
     EXAMPLE 2 
     Let X(t) be governed by a Rayleigh distribution 
     
       
           p ( x )=γy 2   x  exp(−γ x ),γ&gt;0,0 ≦x&lt;∞.   (2.14) 
       
     
     Its centralized version Y(t)=X(t)−2/γ has a probability density 
     
       
           p ( y )=γ(γ y +2)exp(−γ y +2),−2 /γ≦y&lt;∞.   (2.15) 
       
     
     From equation (2.8),                  D   2          (   y   )       =         2                 α     γ            (     y   +     2   γ       )     .               (   2.16   )                         
     The Ito equation for Y(t) is                d                 Y     =         -   α                   Y                      t       +         [         2      α     γ          (     Y   +     2   γ       )       ]       1   /   2                 B        (   t   )                     (   2.17   )                         
     and the correspondence equation for X(t) in the Stratonovich form is                X   .     =         -   α                   X     +       3      α       2      γ       +         (       α   πγ        X     )       1   /   2              ξ        (   t   )       .                 (   2.18   )                         
     Note that the spectral density of X(t) contains a delta function (4/γ 2 ) δ(ω) due to the nonzero mean 2/γ. 
     EXAMPLE 3 
     Consider a family of probability densities, which obeys an equation of the form                          x            p        (   x   )         =       J        (   x   )              p        (   x   )       .               (   2.19   )                         
     Equation (2.19) can be integrated to yield 
     
       
           p ( x )= C   1  exp(∫ J ( x ) dx )  (2.20) 
       
     
     where C 1  is a normalization constant. In this case 
     
       
           D   2 ( x )=−2α exp[− J ( x )]∫ x  exp[ J ( x )] dx.   (2.21) 
       
     
     Several special cases may be noted. Let 
     
       
           J ( x )=−γ x   2   −δx   4   ,−∞&lt;x&lt;∞   (2.22) 
       
     
     where γ can be arbitrary if δ&gt;0. Substitution of equation (2.22) into equation (2.8) leads to                    D   2          (   x   )       =       α   2            π   /   δ            exp        [       δ        (       x   2     +     γ     2      δ         )       2     ]            erfc        [       δ          (       x   2     +     γ     2      δ         )       ]           ,           (   2.23   )                         
     where erfc(y) is the complementary error function defined as                erfc        (   y   )       =       2     π              ∫   y   ∞                 -     t   2                   t     .                   (   2.24   )                         
     The case of γ&lt;0 and δ&gt;0 corresponds to a bimodal distribution, and the case of γ&gt;0 and δ=0 corresponds to a Gaussian distribution. 
     The Pearson family of probability distributions corresponds to                J        (   x   )       =           a   1        x     +     a   0             b   2          x   2       +       b   1        x     +     b   0                 (   2.25   )                         
     In the special case of a 0 +b 1 =0,                  D   2          (   x   )       =       -       2      α         a   1     +     b   2                  (         b   2          x   2       +       b   1        x     +     b   0       )     .               (   2.26   )                         
     From the results of statistical analysis of forming filters with auto-correlation function (1.1) one can describe typical structure of forming filters as in Table 2.1: 
     
       
         
           
               
             
               
                 TABLE 2.1 
               
             
            
               
                   
               
               
                 The Structures of Forming Filters for Typical Probability Density Functions p(x) 
               
            
           
           
               
               
               
            
               
                 Auto-correlation 
                 Probability 
                   
               
               
                 function 
                 density function 
                 Forming filter structure 
               
               
                   
               
               
                 
                   
                     
                       
                         
                           
                             R 
                             y 
                           
                            
                           
                             ( 
                             τ 
                             ) 
                           
                         
                         = 
                         
                           
                             σ 
                             2 
                           
                            
                           
                             e 
                             
                               
                                 - 
                                 α 
                               
                                
                               
                                  
                                 τ 
                                  
                               
                             
                           
                         
                       
                     
                     
                     
                         
                     
                   
                 
                 Gaussian 
                 
                   
                     
                       
                         
                           
                             y 
                             . 
                           
                           + 
                           αy 
                         
                         = 
                         
                           
                             σ 
                             2 
                           
                            
                           
                             ξ 
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                     
                     
                     
                         
                     
                   
                 
               
               
                   
               
               
                 
                   
                     
                       
                         
                           
                             R 
                             y 
                           
                            
                           
                             ( 
                             τ 
                             ) 
                           
                         
                         = 
                         
                           
                             σ 
                             2 
                           
                            
                           
                             e 
                             
                               
                                 - 
                                 α 
                               
                                
                               
                                  
                                 τ 
                                  
                               
                             
                           
                         
                       
                     
                     
                     
                         
                     
                   
                 
                 Uniform 
                 
                   
                     
                       
                         
                           
                             y 
                             . 
                           
                           + 
                           
                             
                               α 
                               2 
                             
                              
                             y 
                           
                         
                         = 
                         
                           
                             
                               σ 
                               2 
                             
                             
                               2 
                                
                               π 
                             
                           
                            
                           
                             
                               α 
                                
                               
                                 ( 
                                 
                                   
                                     Δ 
                                     2 
                                   
                                   - 
                                   
                                     y 
                                     2 
                                   
                                 
                                 ) 
                               
                             
                           
                            
                           
                             ξ 
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                     
                     
                     
                         
                     
                   
                 
               
               
                   
               
               
                 
                   
                     
                       
                         
                           
                             R 
                             y 
                           
                            
                           
                             ( 
                             τ 
                             ) 
                           
                         
                         = 
                         
                           
                             σ 
                             2 
                           
                            
                           
                             e 
                             
                               
                                 - 
                                 α 
                               
                                
                               
                                  
                                 τ 
                                  
                               
                             
                           
                         
                       
                     
                     
                     
                         
                     
                   
                 
                 Rayleigh 
                 
                   
                     
                       
                         
                           
                             y 
                             . 
                           
                           + 
                           
                             αy 
                             ± 
                             
                               
                                 2 
                                  
                                 α 
                               
                               γ 
                             
                           
                         
                         = 
                         
                           
                             
                               σ 
                               2 
                             
                             
                               
                                 2 
                                  
                                 π 
                               
                             
                           
                            
                           
                             
                               
                                 
                                   2 
                                    
                                   α 
                                 
                                 γ 
                               
                                
                               
                                 ( 
                                 
                                   y 
                                   + 
                                   
                                     2 
                                     γ 
                                   
                                 
                                 ) 
                               
                             
                           
                            
                           
                             ξ 
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                     
                     
                     
                         
                     
                   
                 
               
               
                   
               
               
                 
                   
                     
                       
                         
                           
                             R 
                             y 
                           
                            
                           
                             ( 
                             τ 
                             ) 
                           
                         
                         = 
                         
                           
                             σ 
                             2 
                           
                            
                           
                             e 
                             
                               
                                 - 
                                 α 
                               
                                
                               
                                  
                                 τ 
                                  
                               
                             
                           
                         
                       
                     
                     
                     
                         
                     
                   
                 
                 Pearson 
                 
                   
                     
                       
                         
                           
                             y 
                             . 
                           
                           + 
                           αy 
                           + 
                           
                             
                               α 
                               
                                 
                                   a 
                                   1 
                                 
                                 + 
                                 
                                   2 
                                    
                                   
                                     b 
                                     2 
                                   
                                 
                               
                             
                              
                             
                               ( 
                               
                                 
                                   
                                     b 
                                     2 
                                   
                                    
                                   x 
                                 
                                 + 
                                 
                                   b 
                                   1 
                                 
                               
                               ) 
                             
                           
                         
                         = 
                         
                           
                             
                               σ 
                               2 
                             
                             
                               
                                 2 
                                  
                                 π 
                               
                             
                           
                            
                           
                             
                               
                                 
                                   2 
                                    
                                   α 
                                 
                                 
                                   
                                     a 
                                     1 
                                   
                                   + 
                                   
                                     2 
                                      
                                     
                                       b 
                                       2 
                                     
                                   
                                 
                               
                                
                               
                                 ( 
                                 
                                   
                                     
                                       b 
                                       2 
                                     
                                      
                                     
                                       y 
                                       2 
                                     
                                   
                                   + 
                                   
                                     
                                       b 
                                       1 
                                     
                                      
                                     y 
                                   
                                   + 
                                   
                                     b 
                                     0 
                                   
                                 
                                 ) 
                               
                             
                           
                            
                           ξ 
                         
                       
                     
                     
                     
                         
                     
                   
                 
               
               
                   
               
            
           
         
       
     
     The structure of a forming filter with an auto-correlation function given by equations (1.2) and (1.3) is derived as follows. A two-dimensional (2D) system is used to generate a narrow-band stochastic process with the spectrum peak located at a nonzero frequency. The following pair of Ito equations describes a large class of 2D systems: 
     
       
           dx   1 =( a   11   x   1   +a   12   x   2 ) dt+D   1 ( x   1   ,x   2 ) dB   1 ( t ), 
       
     
     
       
           dx   2 =( a   21   x   1   +a   22   x   2 ) dt+D   2 ( x   1   ,x   2 ) dB   2 ( t ),  (3.1) 
       
     
     where B i , i=1,2 are two independent unit Wiener processes. 
     For a system to be stable and to possess a stationary probability density, is required that a 11 &lt;0, a 22 &lt;0 and a 11 a 22 −a 12 a 21 &gt;0. Multiplying (3.1) by x 1 (t−τ) and taking the ensemble average, gives                            τ              R   11          (   τ   )         =         a   11            R   11          (   τ   )         +       a   12            R   12          (   τ   )                  
                      τ              R   12          (   τ   )         =         a   21            R   11          (   τ   )         +       a   22            R   12          (   τ   )                     (   3.2   )                         
     where R 11 (τ)=M[x 1 (t−τ)x 1 (t)], R 12 (τ)=M[x 1 (t−τ)x 2 (t)] with initial conditions R 11 (0)=m 11 =M[x 1   2 ], R 12 (0)=m 12 =M[x 1 x 2 ]. 
     Differential equations (3.2) in the time domain can be transformed (using the Fourier transform) into algebraic equations in the frequency domain as follows                    i                 ω                     R   _     11       -       m   11     π       =         a   11            R   _     11       +       a   12            R   _     12                
                i                 ω                     R   _     12       -       m   12     π       =         a   21            R   _     11       +       a   22            R   _     12           ,             (   3.3   )                         
     where {overscore (R)} ij (ω) define the following integral Fourier transformation:              R   _     ij          (   ω   )       =       Θ        [         R   _     ij          (   τ   )       ]       =       1   π            ∫   0   ∞            R   ij                     (   τ   )               -   iωτ                 τ     .                             
     Then the spectral density S 11 (ω) of x 1 (t) can be obtained as                    S   11          (   ω   )       =         1     2      π              ∫     -   ∞     ∞              R   11          (   τ   )                 -   iωτ               τ           =     R                   e        [         R   _     11          (   ω   )       ]             ,           (   3.4   )                         
     where Re denotes the real part. 
     Since R ij (τ)→0 as τ→∞, it can be shown that          Θ        (              R   ij          (   τ   )              τ       )       =       i                 ω                       R   _     ij          (   ω   )         -       1   π            R   ij          (   0   )                           
     and equation (3.3) is obtained using this relation. 
     Solving equation (3.3) for {overscore (R)} ij (ω) and taking its real part, gives                    S   11          (   ω   )       =           -     (         a   11          m   11       +       a   12          m   12         )                       ω   2       +       A   2          (         a   12          m   12       -       a   22          m   11         )           π        [       ω   4     +       (       A   1   2     -     2        A   2         )          ω   2       +     A   2   2       ]           ,           (   3.5   )                         
     where A 1 =a 11 +a 22 , and A 2 =a 11 a 22 −a 12 a 21 . 
     Expression (3.5) is the general expression for a narrow-band spectral density. The constants a ij , i,j=1,2, can be adjusted to obtain a best fit for a target spectrum. The task is to determine non-negative functions D 1   2 (x 1 x 2 ) and D 2   2 (x 1 x 2 ) for a given p(x 1 ,x 2 ). 
     Forming filters for simulation of non-Gaussian stochastic processes can be derived as follows. The Fokker-Planck-Kolmogorov (FPK) equation for the joint density p(x 1 ,x 2 ) of x 1 (t) and x 2 (t) in the stationary state is given as              ∂     x   1            (         (         a   11          x   1       +       a   12          x   2         )        p     -       1   2            ∂     x   1            [         D   1   2          (       x   1     ,     x   2       )          p     ]           )       +       ∂     x   2            (         (         a   21          x   1       +       a   22          x   2         )        p     -       1   2            ∂     x   2            [         D   2   2          (       x   1     ,     x   2       )          p     ]           )         =   0                   
     If such D 1   2 (x 1 ,x 2 ) and D 2   2 (x 1 ,x 2 ) functions can be found, then the equations of forming filters for the simulation in the Stratonovich form are given by                    x   .     1     =         a   11          x   1       +       a   12          x   2       -       1   4          ∂     x   1              D   1   2          (       x   1     ,     x   2       )         +           D   1          (       x   1     ,     x   2       )           2      π                ξ   1          (   t   )             ,     
              x   .     2     =         a   21          x   1       +       a   22          x   2       -       1   4          ∂     x   2              D   2   2          (       x   1     ,     x   2       )         +           D   2          (       x   1     ,     x   2       )           2      π                ξ   2          (   t   )             ,           (   3.6   )                         
     where ξ i (t), i=1,2, are two independent unit Gaussian white noises. 
     Filters (3.1) and (3.6) are non-linear filters for simulation of non-Gaussian random processes. Two typical examples are provided. 
     EXAMPLE 1 
     Consider two independent uniformly distributed stochastic process x 1  and x 2 , namely,            p        (       x   1     ,     x   2       )       =     1     4        Δ   1          Δ   2           ,                   
     −Δ 1 ≦x 1 ≦Δ 1 , −Δ 2 ≦x 2 ≦Δ 2 . 
     In this case, from the FPK equation, one obtains              a   11     -       1   2            ∂   2       x   1   2            D   1   2       +     a   21     -       1   2            ∂   2       x   2   2            D   2   2         =   0     ,                   
     which is satisfied if 
     
       
           D   1   2   =−a   11 (Δ 1   −x   1   2 ),  D   1   2   =−a   22 (Δ 2   −x   2   2 ). 
       
     
     The two non-linear equations in (3.6) are now                    x   .     1     =         1   2          a   11          x   1       +       a   12          x   2       +           -       a   11       2      π              (       Δ   1     -     x   1   2       )                ξ   1          (   t   )                  
                x   .     2     =         1   2          a   22          x   1       +       a   21          x   2       +           -       a   22       2      π              (       Δ   2     -     x   2   2       )                ξ   2          (   t   )             ,             (   3.7   )                         
     which generate a uniformly distributed stochastic process x 1 (t)with a spectral density given by (3.5). 
     EXAMPLE 2 
     Consider a joint stationary probability density of x 1 (t) and x 2 (t) in the form 
     
       
           p ( x   1   ,x   2 )=ρ(λ)= C   1 (λ+ b ) −δ   ,b &gt;0,δ&gt;1, and  
       
       
         
           
             λ 
             = 
             
               
                 
                   1 
                   2 
                 
                  
                 
                   x 
                   1 
                   2 
                 
               
               - 
               
                 
                   
                     a 
                     12 
                   
                   
                     2 
                      
                     
                       a 
                       21 
                     
                   
                 
                  
                 
                   
                     x 
                     2 
                     2 
                   
                   . 
                 
               
             
           
         
         
         
             
         
       
     
     A large class of probability densities can be fitted in this form. In this case              D   1          (       x   1     ,     x   2       )       =       -       2        a   11         δ   -   1              (     λ   +   b     )         ,         D   2          (       x   1     ,     x   2       )       =         2        a   11          a   12           a   21          (     δ   -   1     )              (     λ   +   b     )               and           p        (     x   1     )       =       C   1            ∫     -   ∞     ∞              (         1   2          x   1   2       -         a   12       2        a   21              u   2       +   b     )     δ               u     .                           
     The forming filter equations (3.6) for this case can be described as following                          x   .     1     =                    a   11          x   1       +       a   12          x   2       -           2        a   11   2           (     δ   -   1     )     2            [         1   2          x   1   2       -         a   12       2        a   21              x   2   2       +   b     ]            x   1       -                                    2        a   11             2      π            (     δ   -   1     )         ·     [         1   2          x   1   2       -         a   12       2        a   21              x   2   2       +   b     ]              ξ   1          (   t   )                      
                    x   .     2     =                    a   21          x   1       +       a   22          x   2       +           2        a   22   2          a   12   3           (     δ   -   1     )     2            [         1   2          x   1   2       -         a   12       2        a   21              x   2   2       +   b     ]            x   2       +         2        a   22          a   12             2      π            (     δ   -   1     )         ·                                  [         1   2          x   1   2       -         a   12       2        a   21              x   2   2       +   b     ]            ξ   2          (   t   )                         (   3.8   )                         
     If σ ik (x,t) are bounded functions (see Appendix I) and the functions F i (x,t) satisfy the Lipshitz condition ∥F(x′−x∥≦K∥x′−x∥, K=const&gt;0, then for every smoothly-varying realization of process y(t) the stochastic equations can be solved by the method of successive substitution which is convergent and defines smoothly-varying trajectories x(t). Thus, Markovian process x(t) has smoothly trajectories with the probability 1. This result can be used as a background in numerical stochastic simulation. 
     The stochastic differential equation for the variable x i  is given by                         x   i            t       =         F   i          (   x   )       +         G   i          (   x   )              ξ   i          (   t   )             ,                i   =   1     ,   2   ,   …              ,   N   ,     x   =       (       x   1     ,     x   2     ,   …              ,     x   N       )     .               (   4.1   )                         
     These equations can be integrated using two different algorithms: Milshtein; and Heun methods. In the Milshtein method, the solution of stochastic differential equation (4.1) is computed by the means of the following recursive relations:                    x   i          (     t   +     δ                 t       )       =         [         F   i          (     x        (   t   )       )       +         σ   2     2            G   i          (     x        (   t   )       )                                G   i          (     x        (   t   )       )                x   i             ]        δ                 t     +     
                         G   i          (     x        (   t   )       )                σ   2        δ                 t              η   i          (   t   )             ,           (   4.2   )                         
     where η i (t) are independent Gaussian random variables and the variance is equal to 1. 
     The second term in equation (4.2) is included because equation (4.2) is interpreted in the Stratonovich sense. The order of numerical error in the Milshtein method is δt . Therefore, small δt(i.e., δt=1×10 −4  for σ 2 =1) is be used, while its computational effort per time step is relatively small. For large σ, where fluctuations are rapid and large, a longer integration period and small δt is used. The Milshtein method quickly becomes impractical. 
     The Heun method is based on the second-order Runge-Kutta method, and integrates the stochastic equation by using the following recursive equation:                        x   i          (     t   +     δ                 t       )       =                    x   i          (   t   )       +         δ                 t     2          [         F   i          (     x        (   t   )       )       +       F   i          (     y        (   t   )       )         ]       +                                        σ   2        δ                 t       2              η   i          (   t   )            [         G   i          (     x        (   t   )       )       +       G   i          (     y        (   t   )       )         ]         ,                   (   4.3   )                         
     where 
     
       
           y   i ( t )= x   i ( t )+ F ( x   i ( t )) δ t+G ( x   i ( t )) {square root over (σ 2   δt )}ρ i ( t ) 
       
     
     The Heun method accepts larger δt than the Milshtein method without a significant increase in computational effort per step. The Heun method is usually used for σ 2 &gt;2. 
     The time step δt can be chosen by using a stability condition, and so that averaged magnitudes do not depend on δt within statistical errors. For example, δt=5×10 −4  for σ 2 =1 and δt=1×10 −5  for σ 2 =15. The Gaussian random numbers for the simulation were generated by using the Box-Muller-Wiener algorithms or a fast numerical inversion method. 
     Table 5.1 summarizes the stochastic simulation of typical road signals. 
     
       
         
           
               
               
               
               
             
               
                 TABLE 5.1 
               
               
                   
               
               
                 Types of 
                 Type of 
                   
                 Results of 
               
               
                 Correlation 
                 Probability 
                 Forming 
                 Stochastic 
               
               
                 Function 
                 Density Function 
                 Filter Equations 
                 Simulations 
               
               
                   
               
             
            
               
                   
                 1D Gaussian 
                   
                   
               
               
                 
                   
                     
                       
                         
                           R 
                            
                           
                             ( 
                             τ 
                             ) 
                           
                         
                         = 
                         
                           
                             σ 
                             2 
                           
                            
                           
                             e 
                             
                               
                                 - 
                                 α 
                               
                                
                               
                                  
                                 τ 
                                  
                               
                             
                           
                         
                       
                     
                     
                     
                         
                     
                   
                 
                 
                   
                     
                       
                         
                           p 
                            
                           
                             ( 
                             y 
                             ) 
                           
                         
                         = 
                         
                           
                             1 
                             
                               σ 
                                
                               
                                 
                                   2 
                                    
                                   π 
                                 
                               
                             
                           
                            
                           
                             e 
                             
                               
                                 - 
                                 
                                   1 
                                   2 
                                 
                               
                                
                               
                                 
                                   ( 
                                   
                                     
                                       y 
                                       - 
                                       μ 
                                     
                                     σ 
                                   
                                   ) 
                                 
                                 2 
                               
                             
                           
                         
                       
                     
                     
                     
                         
                     
                   
                 
                 
                   
                     
                       
                         
                           
                             y 
                             . 
                           
                           + 
                           αy 
                         
                         = 
                         
                           
                             σ 
                             2 
                           
                            
                           
                             ξ 
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                     
                     
                     
                         
                     
                   
                 
                 FIG. 6A 
               
               
                   
               
               
                   
                 1D Uniform 
               
               
                   
                 
                   
                     
                       
                         
                           p 
                            
                           
                             ( 
                             y 
                             ) 
                           
                         
                         = 
                         
                           { 
                           
                             
                               
                                 
                                   0 
                                   , 
                                 
                               
                               
                                 
                                   y 
                                   ∉ 
                                   
                                     [ 
                                     
                                       
                                         y 
                                         0 
                                       
                                       - 
                                       
                                         Δy 
                                         0 
                                       
                                       + 
                                       Δ 
                                     
                                     ] 
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     1 
                                     
                                       2 
                                        
                                       Δ 
                                     
                                   
                                   , 
                                 
                               
                               
                                 
                                   y 
                                   ∈ 
                                   
                                     [ 
                                     
                                       
                                         y 
                                         0 
                                       
                                       - 
                                       
                                         Δy 
                                         0 
                                       
                                       + 
                                       Δ 
                                     
                                     ] 
                                   
                                 
                               
                             
                           
                            
                         
                       
                     
                     
                     
                         
                     
                   
                 
                 
                   
                     
                       
                         
                           
                             y 
                             . 
                           
                           + 
                           
                             
                               α 
                               2 
                             
                              
                             y 
                           
                         
                         = 
                         
                           
                             
                               σ 
                               2 
                             
                             
                               2 
                                
                               π 
                             
                           
                            
                           
                             
                               α 
                                
                               
                                 ( 
                                 
                                   
                                     Δ 
                                     2 
                                   
                                   - 
                                   
                                     y 
                                     2 
                                   
                                 
                                 ) 
                               
                             
                           
                            
                           
                             ξ 
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                     
                     
                     
                         
                     
                   
                 
                 FIG. 6B 
               
               
                   
               
               
                   
                 1D Rayleigh 
               
               
                   
                 
                   
                     
                       
                         
                           p 
                            
                           
                             ( 
                             y 
                             ) 
                           
                         
                         = 
                         
                           
                             ( 
                             
                               y 
                               
                                 μ 
                                 2 
                               
                             
                             ) 
                           
                            
                           
                             e 
                             
                               - 
                               
                                 ( 
                                 
                                   
                                     y 
                                     2 
                                   
                                   
                                     2 
                                      
                                     
                                       μ 
                                       2 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     
                     
                         
                     
                   
                 
                 
                   
                     
                       
                         
                           
                             y 
                             . 
                           
                           + 
                           
                             
                               α 
                               2 
                             
                              
                             y 
                           
                           + 
                           
                             
                               2 
                                
                               α 
                             
                             μ 
                           
                         
                         = 
                         
                           
                             
                               σ 
                               2 
                             
                             
                               
                                 2 
                                  
                                 π 
                               
                             
                           
                            
                           
                             
                               
                                 
                                   2 
                                    
                                   α 
                                 
                                 μ 
                               
                                
                               
                                 ( 
                                 
                                   y 
                                   + 
                                   
                                     2 
                                     μ 
                                   
                                 
                                 ) 
                               
                             
                           
                            
                           
                             ξ 
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                     
                     
                     
                         
                     
                   
                 
                 FIG. 6C 
               
               
                   
               
               
                   
                 2D Gaussian 
               
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 
                                   R 
                                    
                                   
                                     ( 
                                     τ 
                                     ) 
                                   
                                 
                                 = 
                                 
                                   
                                     σ 
                                     2 
                                   
                                    
                                   
                                     e 
                                     
                                       
                                         - 
                                         α 
                                       
                                        
                                       
                                          
                                         τ 
                                          
                                       
                                     
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 [ 
                                 
                                   
                                     cos 
                                      
                                     
                                         
                                     
                                      
                                     ωτ 
                                   
                                   + 
                                   
                                     
                                       α 
                                       ω 
                                     
                                      
                                     sin 
                                      
                                     
                                         
                                     
                                      
                                     ω 
                                      
                                     
                                        
                                       τ 
                                        
                                     
                                   
                                 
                                 ] 
                               
                             
                           
                         
                          
                       
                     
                     
                     
                         
                     
                   
                 
                 
                   
                     
                       
                         
                           p 
                            
                           
                             ( 
                             
                               
                                 y 
                                 1 
                               
                               , 
                               
                                 y 
                                 2 
                               
                             
                             ) 
                           
                         
                         = 
                         
                           
                             1 
                             
                               2 
                                
                               
                                 πσ 
                                 1 
                               
                                
                               
                                 σ 
                                 2 
                               
                             
                           
                            
                           
                             e 
                             
                               
                                 - 
                                 
                                   1 
                                   2 
                                 
                               
                                
                               
                                 ( 
                                 
                                   
                                     
                                       ( 
                                       
                                         
                                           
                                             y 
                                             1 
                                           
                                           - 
                                           
                                             μ 
                                             1 
                                           
                                         
                                         
                                           σ 
                                           1 
                                         
                                       
                                       ) 
                                     
                                     2 
                                   
                                   + 
                                   
                                     
                                       ( 
                                       
                                         
                                           
                                             y 
                                             2 
                                           
                                           - 
                                           
                                             μ 
                                             2 
                                           
                                         
                                         
                                           
                                             σ 
                                             2 
                                           
                                            
                                           
                                               
                                           
                                         
                                       
                                       ) 
                                     
                                     2 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     
                     
                         
                     
                   
                 
                 
                   
                     
                       
                         
                           
                             y 
                             ¨ 
                           
                           + 
                           
                             2 
                              
                             α 
                              
                             
                               y 
                               . 
                             
                           
                           + 
                           
                             
                               ( 
                               
                                 
                                   α 
                                   2 
                                 
                                 + 
                                 
                                   ω 
                                   2 
                                 
                               
                               ) 
                             
                              
                             y 
                           
                         
                         = 
                         
                           
                             
                               2 
                                
                               
                                 
                                   ασ 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       α 
                                       2 
                                     
                                     + 
                                     
                                       ω 
                                       2 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                            
                           
                             ξ 
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                     
                     
                     
                         
                     
                   
                 
                 FIG. 6D 
               
               
                   
               
               
                   
                 2D Uniform 
               
               
                   
                 
                   
                     
                       
                         
                           p 
                            
                           
                             ( 
                             
                               
                                 y 
                                 1 
                               
                               , 
                               
                                 y 
                                 2 
                               
                             
                             ) 
                           
                         
                         = 
                         
                           
                             
                               1 
                               
                                 4 
                                  
                                 
                                   Δ 
                                   1 
                                 
                                  
                                 
                                   Δ 
                                   2 
                                 
                               
                             
                              
                             
                               
 
                             
                             - 
                             
                               Δ 
                               1 
                             
                           
                           &lt; 
                           
                             y 
                             1 
                           
                           &lt; 
                           
                             
                               Δ 
                               1 
                             
                              
                             
                               
 
                             
                             - 
                             
                               Δ 
                               2 
                             
                           
                           &lt; 
                           
                             y 
                             2 
                           
                           &lt; 
                           
                             Δ 
                             2 
                           
                         
                       
                     
                     
                     
                         
                     
                   
                 
                 
                   
                     
                       
                         
                           
                             
                               
                                 
                                   
                                     y 
                                     . 
                                   
                                   1 
                                 
                                 = 
                                 
                                   
                                     
                                       1 
                                       2 
                                     
                                      
                                     
                                       a 
                                       11 
                                     
                                      
                                     
                                       y 
                                       1 
                                     
                                   
                                   + 
                                   
                                     
                                       a 
                                       12 
                                     
                                      
                                     
                                       y 
                                       2 
                                     
                                   
                                   + 
                                   
                                     
                                       
                                         ( 
                                         
                                           
                                             - 
                                             
                                               
                                                 a 
                                                 11 
                                               
                                               
                                                 2 
                                                  
                                                 π 
                                               
                                             
                                           
                                            
                                           
                                             ( 
                                             
                                               
                                                 Δ 
                                                 1 
                                               
                                               - 
                                               
                                                 y 
                                                 1 
                                                 2 
                                               
                                             
                                             ) 
                                           
                                         
                                         ) 
                                       
                                     
                                      
                                     
                                       
                                         ξ 
                                         1 
                                       
                                        
                                       
                                         ( 
                                         t 
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   
                                     y 
                                     . 
                                   
                                   2 
                                 
                                 = 
                                 
                                   
                                     
                                       1 
                                       2 
                                     
                                      
                                     
                                       a 
                                       22 
                                     
                                      
                                     
                                       y 
                                       2 
                                     
                                   
                                   + 
                                   
                                     
                                       a 
                                       21 
                                     
                                      
                                     
                                       y 
                                       1 
                                     
                                   
                                   + 
                                   
                                     
                                       
                                         ( 
                                         
                                           
                                             - 
                                             
                                               
                                                 a 
                                                 22 
                                               
                                               
                                                 2 
                                                  
                                                 π 
                                               
                                             
                                           
                                            
                                           
                                             ( 
                                             
                                               
                                                 Δ 
                                                 2 
                                               
                                               - 
                                               
                                                 y 
                                                 2 
                                                 2 
                                               
                                             
                                             ) 
                                           
                                         
                                         ) 
                                       
                                     
                                      
                                     
                                       
                                         ξ 
                                         1 
                                       
                                        
                                       
                                         ( 
                                         t 
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                           
                         
                          
                       
                     
                     
                     
                         
                     
                   
                 
                 FIG. 6E 
               
               
                   
               
               
                   
                 2D Hyperbolic 
               
               
                   
                 
                   
                     
                       
                         
                           
                             
                               
                                 
                                   p 
                                    
                                   
                                     ( 
                                     
                                       
                                         y 
                                         1 
                                       
                                       , 
                                       
                                         y 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 = 
                               
                             
                           
                           
                             
                               
                                 
                                   ρ 
                                    
                                   
                                     ( 
                                     λ 
                                     ) 
                                   
                                 
                                 = 
                                 
                                   
                                     
                                       C 
                                       1 
                                     
                                      
                                     
                                       ( 
                                       
                                         λ 
                                         + 
                                         b 
                                       
                                       ) 
                                     
                                   
                                   
                                     - 
                                     δ 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   b 
                                   &gt; 
                                   0 
                                 
                                 ; 
                                 
                                   δ 
                                   &gt; 
                                   1 
                                 
                               
                             
                           
                           
                             
                               
                                 λ 
                                 = 
                                 
                                   
                                     
                                       1 
                                       2 
                                     
                                      
                                     
                                       y 
                                       1 
                                       2 
                                     
                                   
                                   - 
                                   
                                     
                                       
                                         a 
                                         12 
                                       
                                       
                                         2 
                                          
                                         
                                           a 
                                           21 
                                         
                                       
                                     
                                      
                                     
                                       y 
                                       2 
                                       2 
                                     
                                   
                                 
                               
                             
                           
                         
                          
                       
                     
                     
                     
                         
                     
                   
                 
                 
                   
                     
                       
                         
                           
                             
                               
                                 
                                   
                                     y 
                                     . 
                                   
                                   1 
                                 
                                 = 
                                 
                                   
                                     
                                       a 
                                       11 
                                     
                                      
                                     
                                       y 
                                       1 
                                     
                                   
                                   + 
                                   
                                     
                                       a 
                                       12 
                                     
                                      
                                     
                                       y 
                                       2 
                                     
                                      
                                     
                                       
                                         
                                           2 
                                            
                                           
                                             a 
                                             11 
                                             2 
                                           
                                         
                                         
                                           
                                             ( 
                                             
                                               δ 
                                               - 
                                               1 
                                             
                                             ) 
                                           
                                           2 
                                         
                                       
                                        
                                       
                                         [ 
                                         
                                           
                                             
                                               1 
                                               2 
                                             
                                              
                                             
                                               y 
                                               1 
                                               2 
                                             
                                              
                                             
                                               
                                                 a 
                                                 12 
                                               
                                               
                                                 2 
                                                  
                                                 
                                                   a 
                                                   21 
                                                 
                                               
                                             
                                              
                                             
                                               y 
                                               2 
                                               2 
                                             
                                           
                                           + 
                                           b 
                                         
                                         ] 
                                       
                                     
                                      
                                     
                                       y 
                                       1 
                                     
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   
                                     
                                       2 
                                        
                                       
                                         a 
                                         11 
                                       
                                     
                                     
                                       
                                         
                                           2 
                                            
                                           π 
                                         
                                       
                                        
                                       
                                         ( 
                                         
                                           δ 
                                           - 
                                           1 
                                         
                                         ) 
                                       
                                     
                                   
                                    
                                   
                                     [ 
                                     
                                       
                                         
                                           1 
                                           2 
                                         
                                          
                                         
                                           y 
                                           1 
                                           2 
                                         
                                          
                                         
                                           
                                             a 
                                             12 
                                           
                                           
                                             2 
                                              
                                             
                                               a 
                                               21 
                                             
                                           
                                         
                                          
                                         
                                           y 
                                           2 
                                           2 
                                         
                                       
                                       + 
                                       b 
                                     
                                     ] 
                                   
                                 
                                  
                                 
                                   
                                     ξ 
                                     1 
                                   
                                    
                                   
                                     ( 
                                     t 
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   
                                     y 
                                     . 
                                   
                                   2 
                                 
                                 = 
                                 
                                   
                                     
                                       a 
                                       21 
                                     
                                      
                                     
                                       y 
                                       1 
                                     
                                   
                                   + 
                                   
                                     
                                       a 
                                       22 
                                     
                                      
                                     
                                       y 
                                       2 
                                     
                                   
                                   + 
                                   
                                     
                                       
                                         
                                           2 
                                            
                                           
                                             a 
                                             22 
                                             2 
                                           
                                            
                                           
                                             a 
                                             12 
                                             3 
                                           
                                         
                                         
                                           
                                             
                                               a 
                                               21 
                                               3 
                                             
                                              
                                             
                                               ( 
                                               
                                                 δ 
                                                 - 
                                                 1 
                                               
                                               ) 
                                             
                                           
                                           2 
                                         
                                       
                                        
                                       
                                         [ 
                                         
                                           
                                             
                                               1 
                                               2 
                                             
                                              
                                             
                                               y 
                                               1 
                                               2 
                                             
                                              
                                             
                                               
                                                 a 
                                                 12 
                                               
                                               
                                                 2 
                                                  
                                                 
                                                   a 
                                                   21 
                                                 
                                               
                                             
                                              
                                             
                                               y 
                                               2 
                                               2 
                                             
                                           
                                           + 
                                           b 
                                         
                                         ] 
                                       
                                     
                                      
                                     
                                       y 
                                       2 
                                     
                                   
                                   + 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   
                                     
                                       2 
                                        
                                       
                                         a 
                                         22 
                                       
                                        
                                       
                                         a 
                                         12 
                                       
                                     
                                     
                                       
                                         
                                           2 
                                            
                                           π 
                                         
                                       
                                        
                                       
                                         
                                           a 
                                           21 
                                         
                                          
                                         
                                           ( 
                                           
                                             δ 
                                             - 
                                             1 
                                           
                                           ) 
                                         
                                       
                                     
                                   
                                    
                                   
                                     [ 
                                     
                                       
                                         
                                           1 
                                           2 
                                         
                                          
                                         
                                           y 
                                           1 
                                           2 
                                         
                                          
                                         
                                           
                                             a 
                                             12 
                                           
                                           
                                             2 
                                              
                                             
                                               a 
                                               21 
                                             
                                           
                                         
                                          
                                         
                                           y 
                                           2 
                                           2 
                                         
                                       
                                       + 
                                       b 
                                     
                                     ] 
                                   
                                 
                                  
                                 
                                   
                                     ξ 
                                     2 
                                   
                                   ( 
                                   t 
                                 
                               
                             
                           
                         
                          
                       
                     
                     
                     
                         
                     
                   
                 
                 FIG. 6F 
               
               
                   
               
            
           
         
       
     
     FIG. 7 shows a vehicle body  710  with coordinates for describing position of the body  710  with respect to wheels  701 - 704  and suspension system. A global reference coordinate x r , y r , z r {r} is assumed to be at the geometric center P r  of the vehicle body  710 . The following are the transformation matrices to describe the local coordinates for the suspension and its components: 
     {2} is a local coordinate in which an origin is the center of gravity of the vehicle body  710 ; 
     {7} is a local coordinate in which an origin is the center of gravity of the suspension; 
     {10n} is a local coordinate in which an origin is the center of gravity of the n&#39;th arm; 
     {12n} is a local coordinate in which an origin is the center of gravity of the n&#39;th wheel; 
     {13n} is a local coordinate in which an origin is a contact point of the n&#39;th wheel relative to the road surface; and 
     {14} is a local coordinate in which an origin is a connection point of the stabilizer. 
     Note that in the development that follows, the wheels  702 ,  701 ,  704 , and  703  are indexed using “i”, “ii”, “iii”, and “iv”, respectively. 
     As indicated, “n” is a coefficient indicating wheel positions such as i, ii, iii, and iv for left front, right front, left rear and right rear respectively. The local coordinate systems x 0 , y 0 , and z 0 {0} are expressed by using the following conversion matrix that moves the coordinate {r} along a vector (0,0,z 0 )                  0   r        T   =     [         1       0       0       0           0       1       0       0           0       0       1         z   0             0       0       0       1         ]                     
     Rotating the vector {r} along y r  with an angle β makes a local coordinate system x 0c , y 0c , z 0c {0r} with a transformation matrix  0c   0 T.                          0      c                  0          T   =     [           cos                 β         0         sin                 β         0           0       1       0       0               -   sin                   β         0         cos                 β         0           0       0       0       1         ]             (   5.1   )                         
     Transferring {0r} through the vector (a 1n , 0,0) makes a local coordinate system x 0f , y 0f , z 0f {0f} with a transformation matrix  0r   0f T.                          0      n       0      c          T   =     [         1       0       0         a     1      n               0       1       0       0           0       0       1       0           0       0       0       1         ]             (   5.2   )                         
     The above procedure is repeated to create other local coordinate systems with the following transformation matrices.                          1      n       0      n          T   =     [         1       0       0       0           0         cos                 α             -   sin                   α         0           0         sin                 α           cos                 α         0           0       0       0       1         ]             (   5.3   )                         2     1      i          T   =     [         1       0       0         a   0             0       1       0         b   0             0       0       1         c   0             0       0       0       1         ]             (   5.4   )                         
     Coordinates for the wheels (index n: i for the left front, ii for the right front, etc.) are generated as follows. Transferring {1n} through the vector (0, b 2n , 0) makes local coordinate system x 3n , y 3n , z 3n {3n} with transformation matrix  1f   3n T.                          3      n       1      n          T   =     [         1       0       0       0           0       1       0         b     2      n               0       0       1       0           0       0       0       1         ]             (   5.5   )                           4      n       3      n          T   =     [         1       0       0       0           0         cos                   γ   n               -   sin                     γ   n           0           0         sin                   γ   n             cos                   γ   n           0           0       0       0       1         ]             (   5.6   )                           5      n       4      n          T   =     [         1       0       0       0           0       1       0       0           0       0       1         c     1      n               0       0       0       1         ]             (   5.7   )                           6      n       5      n          T   =     [         1       0       0       0           0         cos                   η   n               -   sin                     η   n           0           0         sin                   η   n             cos                   η   n           0           0       0       0       1         ]             (   5.8   )                           7      n       6      n          T   =     [         1       0       0       0           0       1       0       0           0       0       1         z     6      n               0       0       0       1         ]             (   5.9   )                           8      n       4      n          T   =     [         1       0       0       0           0       1       0       0           0       0       1         c     2      n               0       0       0       1         ]             (   5.10   )                           9      n       8      n          T   =     [         1       0       0       0           0         cos                   θ   n               -   sin                     θ   n           0           0         sin                   θ   n             cos                   θ   n           0           0       0       0       1         ]             (   5.11   )                           10      n                    9      n            T   =     [         1       0       0       0           0       1       0         e     1      n               0       0       1       0           0       0       0       1         ]             (   5.12   )                           11      n                    9      n            T   =     [         1       0       0       0           0       1       0         e     3      n               0       0       1       0           0       0       0       1         ]             (   5.13   )                           12      n       11      n          T   =     [         1       0       0       0           0         cos                   ζ   n               -   sin                     ζ   n           0           0         sin                   ζ   n             cos                   ζ   n           0           0       0       0       1         ]             (   5.14   )                             13      n       12      n          T     =     [         1       0       0       0           0       1       0       0           0       0       1         z     12      n               0       0       0       1         ]             (   5.15   )                           14      n                    9      n            T   =     [         1       0       0       0           0       1       0         e     0      n               0       0       1       0           0       0       0       1         ]             (   5.16   )                         
     Some of the matrices are sub-assembled to make the calculation simpler.                              1      n                  r          T     =                          0   r        T                  0      n       0      c          T                  1      n       0      n          T       =           [         1       0       0       0           0       1       0       0           0       0       1         z   0             0       0       0       1         ]          [           cos                 β         0         sin                 β         0           0       1       0       0               -   sin                   β         0         cos                 β         0           0       0       0       1         ]            [         1       0       0         a     1      n               0       1       0       0           0       0       1       0           0       0       0       1         ]            [         1       0       0       0           0         cos                 α             -   sin                   α         0           0         sin                 α           cos                 α         0           0       0       0       1         ]                     =                  [           cos                 β         0         sin                 β             a     1      n          cos                 β             0       1       0       0               -   sin                   β         0         cos                 β             z   0     -       a   1        sin                 β               0       0       0       1         ]          [         1       0       0       0           0         cos                 α             -   sin                   α         0           0         sin                 α           cos                 α         0           0       0       0       1         ]                   =                [           cos                 β           sin                 β                 sin                 α           sin                 β                 cos                 α             a     1      n          cos                 β             0         cos                 α             -   sin                   α         0               -   sin                   β           cos                 β                 sin                 α           cos                 β                 cos                 α             z   0     -       a     1      n          sin                 β               0       0       0       1         ]                   (   5.17   )                               4      n                  r          T     =                            1      n                  r          T                  3      n       1      n          T                  4      n       3      n          T       =         [           cos                 β           sin                 β                 sin                 α           sin                 β                 cos                 α             a     1      n          cos                 β             0         cos                 α             -   sin                   α         0               -   sin                   β           cos                 β                 sin                 α           cos                 β                 cos                 α             z   0     -       a     1      n          sin                 β               0       0       0       1         ]          [         1       0       0       0           0       1       0         b     2      n               0       0       1       0           0       0       0       1         ]       ·     [         1       0       0       0           0         cos                   γ   n               -   sin                     γ   n           0           0         sin                   γ   n             cos                   γ   n           0           0       0       0       1         ]                     =                [           cos                 β           sin                 β                   sin        (     α   +     γ   n       )               sin                 β                   cos        (     α   +     γ   n       )                   b     2      n          sin                 β                 sin                 α     +       a     1      n          cos                 β               0         cos                   (     α   +     γ   n       )             -     sin        (     α   +     γ   n       )                 b     2      n          cos                 α                 -   sin                   β           cos                 β                   sin        (     α   +     γ   n       )               cos                 β                   cos        (     α   +     γ   n       )                 z   0     -       b     2      n          cos                 β                 sin                 α                -       a     1      n          sin                 β               0       0       0       1         ]                   (   5.18   )                               7      n       4      n          T     =                            5      n       4      n          T                  6      n       5      n          T                  7      n       6      n          T       =         [         1       0       0       0           0       1       0       0           0       0       1         c     1      n               0       0       0       1         ]          [         1       0       0       0           0         cos                   η   n               -   sin                     η   n           0           0         sin                   η   n             cos                   η   n           0           0       0       0       1         ]            [         1       0       0       0           0       1       0       0           0       0       1         z     6      n               0       0       0       1         ]                     =                  [         1       0       0       0           0         cos                   η   n               -   sin                     η   n           0           0         sin                   η   n             cos                   η   n             c     1      n               0       0       0       1         ]          [         1       0       0       0           0       1       0       0           0       0       1         z     6      n               0       0       0       1         ]                   =                [         1       0       0       0           0         cos                   η   n               -   sin                     η   n               -     z     6      n            sin                   η   n               0         sin                   η   n             cos                   η   n               c     1      n       +       z     6      n          cos                   η   n                 0       0       0       1         ]                   (   5.19   )                               10      n                    4      n            T     =                            8      n       4      n          T                  9      n       8      n          T                  10      n                    9      n            T       =         [         1       0       0       0           0       1       0       0           0       0       1         c     2      n               0       0       0       1         ]          [         1       0       0       0           0         cos                   θ   n               -   sin                     θ   n           0           0         sin                   θ   n             cos                   θ   n           0           0       0       0       1         ]            [         1       0       0       0           0       1       0         e     1      n               0       0       1       0           0       0       0       1         ]                     =                  [         1       0       0       0           0         cos                   θ   n               -   sin                     θ   n           0           0         sin                   θ   n             cos                   θ   n             c     2      n               0       0       0       1         ]          [         1       0       0       0           0       1       0         e     1      n               0       0       1       0           0       0       0       1         ]                   =                [         1       0       0       0           0         cos                   θ   n               -   sin                     θ   n               e     1      n          cos                   θ   n               0         sin                   θ   n             cos                   θ   n               c     2      n       +       e     1      n          sin                   θ   n                 0       0       0       1         ]                   (   5.20   )                               10      n                    4      n            T     =                            8      n       4      n          T                  9      n       8      n          T          T     12      n       11      n           11      n                    9      n            T     =           [         1       0       0       0           0       1       0       0           0       0       1         c     2      n               0       0       0       1         ]          [         1       0       0       0           0         cos                   θ   n               -   sin                     θ   n           0           0         sin                   θ   n             cos                   θ   n           0           0       0       0       1         ]            [         1       0       0       0           0       1       0         e     3      n               0       0       1       0           0       0       0       1         ]                  [         1       0       0       0           0         cos                   ζ   n               -   sin                     ζ   n           0           0         sin                   ζ   n             cos                   ζ   n           0           0       0       0       1         ]                   =                    [         1       0       0       0           0         cos                   θ   n               -   sin                     θ   n           0           0         sin                   θ   n             cos                   θ   n             c     2      n               0       0       0       1         ]          [         1       0       0       0           0       1       0         e     3      n               0       0       1       0           0       0       0       1         ]                  [         1       0       0       0           0         cos                   ζ   n               -   sin                     ζ   n           0           0         sin                   ζ   n             cos                   ζ   n           0           0       0       0       1         ]                 =                  [         1       0       0       0           0         cos                   θ   n               -   sin                     θ   n               e     3      n          cos                   θ   n               0         sin                   θ   n             cos                   θ   n               c     2      n       +       e     3                 n          sin                   θ   n                 0       0       0       1         ]          [         1       0       0       0           0         cos                   ζ   n               -   sin                     ζ   n           0           0         sin                   ζ   n             cos                   ζ   n           0           0       0       0       1         ]                   =                [         1       0       0       0           0         cos        (       θ   n     +     ζ   n       )               -   sin                     (       θ   n     +     ζ   n       )               e     3      n          cos                   θ   n               0         sin                   (       θ   n     +     ζ   n       )             cos        (       θ   n     +     ζ   n       )               c     2      n       +       e     3                 n          sin                   θ   n                 0       0       0       1         ]                   (   5.21   )                         
     Parts of the model are described both in local coordinate systems and in relations to the coordinate {r} or {1n} referenced to the vehicle body  710 . 
     In the local coordinate systems:                P   body   2     =       P     susp   .   n       7      n       =       P     arm   .   n       10      n       =       P     wheel   .   n       12      n       =       P     touchpoint   .   n       13      n       =       P     stab   .   n       14      n       =     [         0           0           0           1         ]                       (   5.22   )                         
     In the global reference coordinate system {r}:                      P   body   r     =                 1      i     r        T          TP   body   2       2     1      i         =         [           cos                 β           sin                 βsin                 α           sin                 βcos                 α             a     1      i          cos                 β             0         cos                 α             -   sin                   α         0               -   sin                   β           cos                 βsin                 α           cos                 βcos                 α             z   0     -       a     1      i          sin                 β               0       0       0       1         ]          [         1       0       0         a   0             0       1       0         b   0             0       0       1         c   0             0       0       0       1         ]            [         0           0           0           1         ]                     =     [                            a   0        cos                 β     +       b   0        sin                 βsinα     +       c   0        sin                 βcosα     +       a     1      i          cos                 β                                    b   0        cos                 α     -       c   0        sin                 α                       -     a   0          sin                 β     +       b   0        cos                 βsinα     +       c   0        cos                 βcosα     -       a     1      i          sin                 β                            1           ]                   (   5.23   )                       P     susp   .   n     r     =                            4      n     r        T          TP     susp   .   n       7      n           7      n       4      n         =                  [           cos                 β           sin                 βsin                   (     α   +     γ   n       )             sin                 βcos                   (     α   +     γ   n       )                 b     2      n          sin                 βsin                 α     +       a     1      n          cos                 β               0         cos                   (     α   +     γ   n       )               -   sin                     (     α   +     γ   n       )               b     2      n          cos                 α                 -   sin                   β           cos                   βsin        (     α   +     γ   n       )               cos                 βcos                   (     α   +     γ   n       )               z   0     +       b     2      n          cos                 βsin                 α     -       a     1      n          sin                 β               0       0       0       1         ]     ·                                  [         1       0       0       0           0         cos                   η   n               -   sin                     η   n               -     z     6      n            sin                   η   n               0         sin                   η   n             cos                   η   n               c     1      n       +       z     6      n          cos                   η   n                 0       0       0       1         ]          [         0           0           0           1         ]                   =                [               {         z     6      n            cos        (     α   +     γ   n     +     η   n       )         +       c     1      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }        sin                 β     +       a     1      n          cos                 β                                  -     z     6      n              sin        (     α   +     γ   n     +     η   n       )         -       c     1      n            sin        (     α   +     γ   n       )         +       b     2      n          cos                 α                       {         z     6      n            cos        (     α   +     γ   n     +     η   n       )         +       c     1      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }        cos                 β     -       a     1      n          sin                 β                            1           ]                   (   5.24   )                       P     arm   .   n     r     =                            4      n     r        T          TP     arm   .   n       10      n           10      n       4      n         =       [           cos                 β           sin                 βsin                   (     α   +     γ   n       )             sin                 βcos                   (     α   +     γ   n       )                 b     2      n          sin                 βsin                 α     +       a     1      n          cos                 β               0         cos                   (     α   +     γ   n       )               -   sin                     (     α   +     γ   n       )               b     2      n          cos                 α                 -   sin                   β           cos                   βsin        (     α   +     γ   n       )               cos                 βcos                   (     α   +     γ   n       )               z   0     +       b     2      n          cos                 βsin                 α     -       a     1      n          sin                 β               0       0       0       1         ]     ·                                  [         1       0       0       0           0         cos                   θ   n               -   sin                     θ   n               e     3      n          cos                   θ   n               0         sin                   θ   n             cos                   θ   n               c     2      n       +       e     1      n          sin                   θ   n                 0       0       0       1         ]          [         0           0           0           1         ]                   =                [               {         e     1      n            sin        (     α   +     γ   n     +     θ   n       )         +       c     2      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }        sin                 β     +       a     1      n          cos                 β                                  e     1      n            cos        (     α   +     γ   n     +     θ   n       )         -       c     2      n            sin        (     α   +     γ   n       )         +       b     2      n          cos                 α                       {         e     1      n            sin        (     α   +     γ   n     +     θ   n       )         +       c     2      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }        cos                 β     -       a     1      n          sin                 β                            1           ]                   (   5.25   )                       P     wheel   .   n     r     =                            4      n     r        T          TP     wheel   .   n       12      n           12      n       4      n         =     [           cos                 β           sin                 βsin                   (     α   +     γ   n       )             sin                 βcos                   (     α   +     γ   n       )                 b     2      n          sin                 βsin                 α     +       a     1      n          cos                 β               0         cos                   (     α   +     γ   n       )               -   sin                     (     α   +     γ   n       )               b     2      n          cos                 α                 -   sin                   β           cos                   βsin        (     α   +     γ   n       )               cos                 βcos                   (     α   +     γ   n       )                 b     2      n          cos                 βsin                 α     -       a     1      n          sin                 β               0       0       0       1         ]                                  [         1       0       0       0           0         cos        (       θ   n     +     ζ   n       )             -     sin        (       θ   n     +     ζ   n       )                 e     3      n          cos                   θ   n               0         sin        (       θ   n     +     ζ   n       )             cos        (       θ   n     +     ζ   n       )               c     2      n       +       e     3      n          sin                   θ   n                 0       0       0       1         ]          [         0           0           0           1         ]                   =                [               {         e     3      n            sin        (     α   +     γ   n     +     θ   n       )         +       c     2      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }        sin                 β     +       a     1      n          cos                 β                                  e     3      n            cos        (     α   +     γ   n     +     θ   n       )         -       c     2      n            sin        (     α   +     γ   n       )         +       b     2      n          cos                 α                     z   0     +       {         e     3      n            sin        (     α   +     γ   n     +     θ   n       )         +       c     2      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }        cos                 β     -       a     1      n          sin                 β                            1           ]                   (   5.26   )                       P     touchpoint   .   n     r     =                            4      n     r        T          T     13      n       12      n           12      n       4      n            TP     touchpoint   .   n       13      n         =                [           cos                 β           sin                 βsin                   (     α   +     γ   n       )             sin                 βcos                   (     α   +     γ   n       )                 b     2      n          sin                 βsin                 α     +       a     1      n          cos                 β               0         cos                   (     α   +     γ   n       )               -   sin                     (     α   +     γ   n       )               b     2      n          cos                 α                 -   sin                   β           cos                   βsin        (     α   +     γ   n       )               cos                 βcos                   (     α   +     γ   n       )               z   0     +       b     2      n          cos                 βsin                 α     -       a     1      n          sin                 β               0       0       0       1         ]                                    [         1       0       0       0           0         cos        (       θ   n     +     ζ   n       )             -     sin        (       θ   n     +     ζ   n       )                 e     3      n          cos                   θ   n               0         sin        (       θ   n     +     ζ   n       )             cos        (       θ   n     +     ζ   n       )               c     2      n       +       e     3      n          sin                   θ   n                 0       0       0       1         ]          [         1       0       0       0           0       1       0       0           0       0       1         z     12      n               0       0       0       1         ]            [         0           0           0           1         ]                   =                [               {         z     12      n          cos                 α     +       e     3      n            sin        (     α   +     γ   n     +     θ   n       )         +       c     2      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }        sin                 β     +       a     1      n          cos                 β                                  -     z     12      n            sin                 α     +       e     3      n            cos        (     α   +     γ   n     +     θ   n       )         -       c     2      n            sin        (     α   +     γ   n       )         +       b     2      n          cos                 α                     z   0     +       {         z     12      n          cos                 α     +       e     3      n            sin        (     α   +     γ   n     +     θ   n       )         +       c     2      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }        cos                 β     -       a     1      n          sin                 β                            1           ]                   (   5.27   )                         
     where ζ n  is substituted by, 
     
       
         ζ n =−γ n −θ n   
       
     
     because of the link mechanism to support a wheel at this geometric relation. 
     The stabilizer linkage point is in the local coordinate system {1n}. The stabilizer works as a spring in which force is proportional to the difference of displacement between both arms in a local coordinate system {1n} fixed to the body  710 .                      P     stab   .   n       1      n       =                          3      n       1      n          T                  4      n       3      n          T                  8      n       4      n          T                  9      n       8      n          T          TP     stab   .   n       14      n           14      n       9      n                     =                    [         1       0       0       0           0       1       0         b     2      n               0       0       1       0           0       0       0       1         ]          [         1       0       0       0           0         cos                   γ   n               -   sin                     γ   n           0           0         sin                   γ   n             cos                   γ   n           0           0       0       0       1         ]            [         1       0       0       0           0       1       0       0           0       0       1         c     2      n               0       0       0       1         ]                                    [         1       0       0       0           0         cos                   θ   n               -   sin                     θ   n           0           0         sin                   θ   n             cos                   θ   n           0           0       0       0       1         ]          [         1       0       0       0           0       1       0         e     0      n               0       0       1       0           0       0       0       1         ]            [         0           0           0           1         ]                   =                [                      0                   e     0      n            cos        (       γ   n     +     θ   n       )         -       c     2      n          sin                   γ   n       +     b     2      n                                    e     0      n            sin        (       γ   n     +     θ   n       )         +       c     2      n          cos                   γ   n                                0           ]                   (   5.28   )                         
     Kinetic energy, potential energy and dissipative functions for the &lt;Body&gt;, &lt;Suspension&gt;, &lt;Arm&gt;, &lt;Wheel&gt; and &lt;Stabilizer&gt; are developed as follows. Kinetic energy and potential energy except by springs are calculated based on the displacement referred to the inertial global coordinate {r}. Potential energy by springs and dissipative functions are calculated based on the movement in each local coordinate.                &lt;        Body        &gt;                               T   b   tr     =       1   2            m   b          (         x   .     b   2     +       y   .     b   2     +       z   .     b   2       )                 (   5.29   )             where                                 x   b     =         (       a   0     +     a     1      n         )        cos                 β     +       (         b   0        sin                 α     +       c   0        cos                 α       )        sin                 β                     y   b     =         b   0        cos                 α     -       c   0        sin                 α                     z   b     =       z   0     -       (       a   0     +     a     1      n         )        sin                 β     +       (         b   0        sin                 α     +       c   0        cos                 α       )        cos                 β                     (   5.30   )             and                                   q     j   ,   k       =   β     ,   α   ,     z   0                     ∂     x   b         ∂   β       =         -     (       a   0     +     a     1      n         )          sin                 β     +       (         b   0        sin                 α     +       c   0        cos                 α       )        cos                 β                       ∂     x   b         ∂   α       =       (         b   0        cos                 α     -       c   0        sin                 α       )        sin                 β                     ∂     y   b         ∂   β       =         ∂     x   b         ∂     z   0         =         ∂     y   b         ∂     z   0         =   0                       ∂     y   b         ∂   α       =         -     b   0          sin                 α     -       c   0        cos                 α                       ∂     z   b         ∂   β       =         -     (       a   0     +     a     1      n         )          cos                 β     -       (         b   0        sin                 α     +       c   0        cos                 α       )        sin                 β                       ∂     z   b         ∂   α       =       (         b   0        cos                 α     -       c   0        sin                 α       )        cos                 β                     ∂     z   b         ∂     z   0         =   1                 (   5.31   )               and                 thus                                     T   b   tr     =                  1   2            m   b          (         x   .     b   2     +       y   .     b   2     +       z   .     b   2       )                                  =                  1   2          m   b            ∑                 j   ,   k                         (           ∂     x   b         ∂     q   j                ∂     x   b         ∂     q   k                q   .     j            q   .     k       +         ∂     y   b         ∂     q   j                ∂     y   b         ∂     q   k                q   .     j            q   .     k       +         ∂     z   b         ∂     q   j                ∂     z   b         ∂     q   k                q   .     j            q   .     k         )                   =                  1   2          m   b          〈           β   .     2            {         -     (       a   0     +     a   1       )          sin                 β     +       (         b   0        sin                 α     +       c   0        cos                 α       )        cos                 β       }     2       +                                        α   .     2            {       (         b   0        cos                 α     -       c   0        sin                 α       )        sin                 β     }     2       +           α   .     2          (         -     b   0          sin                 α     -       c   0        cos                 α       )       2     +                                    β   .     2            {         -     (       a   0     +     a   1       )          cos                 β     -       (         b   0        sin                 α     +       c   0        cos                 α       )        sin                 β       }     2       +                                    α   .     2            {       (         b   0        cos                 α     -       c   0        sin                 α       )        cos                 β     }     2       +       z   .     0   2     +     2        α   .            β   .     [     {         -     (       a   0     +     a   1       )          sin                 β     +                                              (         b   0        sin                 α     +       c   0        cos                 α       )        cos                 β     }            (         b   0        cos                 α     -       c   0        sin                 α       )        sin                 β     +     {         -     (       a   0     +     a   1       )          cos                 β     -                                          (         b   0        sin                 α     +       c   0        cos                 α       )        sin                 β     }            (         b   0        cos                 α     -       c   0        sin                 α       )        cos                 β     ]     -     2        β   .            z   .     o          {         (       a   0     +     a     1      n         )        cos                 β     +                                          (         b   0        sin                 α     -       c   0        cos                 α       )        sin                 β     }       +     2        α   .              z   .     0          (         b   0        cos                 α     -       c   0        sin                 α       )          cos                 β       〉               =                  1   2          m   b          〈           α   .     2          (       b   0   2     +     c   0   2       )       +         β   .     2          {         (       a   0     +     a     1      i         )     2     +       (         b   0        sin                 α     +       c   0        cos                 α       )     2       }       +       z   .     0   2     -                                    2        α   .            β   .          (       a   0     +     a     1      i         )            (         b   0        cos                 α     -       c   0        sin                 α       )       -     2        β   .            z   .     o          {         (       a   0     +     a     1      i         )        cos                 β     +                                          (         b   0        sin                 α     -       c   0        cos                 α       )        sin                 β     +     2        α   .              z   .     o          (         b   0        cos                 α     -       c   0        sin                 α       )          cos                 β       〉                   (   5.32   )                 T   b   ro     =                  1   2          (         I   bx          ω   bx   2       +       I   by          ω   by   2       +       I   bz          ω   bz   2         )                             where                           ω     b                 x       =     α   .                               ω     b                 y       =     β   .                               ω     b                 z       =   0                         ∴                           T   b   ro     =                  1   2          (         I   bx            α   .     2       +       I   by            β   .     2         )                                       U   b     =       m   b        g                   z   b                   =       m   b        g        {         -     (       a   0     +     a     1                 n         )          sinβ     +       (         b   0        sin                 α     +       c   0        cos                 α       )        cos                 β       }                     (   5.33   )                 &lt;        Suspension        &gt;                               T     s                 n                    t                 r         =       1   2            m     s                 n            (         x   .       s                 n     2     +       y   .       s                 n     2     +       z   .       s                 n     2       )          `             (   5.34   )             where                                 x   sn     =                    {         z     6      n            cos        (     α   +     γ   n     +     η   n       )         +       c     1      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }        sin                 β     +       a     1      n          cos                 β                     y   sn     =                    -     z     6      n              sin        (     α   +     γ   n     +     η   n       )         -       c     1      n            sin        (     α   +     γ   n       )         +       b     2      n          cos                 α                     z   sn     =                  z   0     +       {         z     6      n            cos        (     α   +     γ   n     +     η   n       )         +       c     1      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }        cos                 β     -       a     1      n          sin                 β                                         q     j   ,   k       =     z     6      n         ,     η   n     ,   α   ,   β   ,     z   0             (   5.35   )                   ∂     x   sn         ∂     z     6      n           =       cos        (     α   +     γ   n     +     η   n       )          sin                 β                                 ∂     x   sn         ∂     η   n         =       -     z     6      n              sin        (     α   +     γ   n     +     η   n       )          sin                 β                                 ∂     x   sn         ∂   α       =       {         -     z     6      n              sin        (     α   +     γ   n     +     η   n       )         -       c     1      n            sin        (     α   +     γ   n       )         +       b     2      n          cos                 α       }        sin                 β                                 ∂     x   sn         ∂   β       =         {         z     6      n            cos        (     α   +     γ   n     +     η   n       )         +       c     1      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }        cos                 β     -       a     1      n          sin                 β                                   ∂     y   sn         ∂     z     6      n           =     -     sin        (     α   +     γ   n     +     η   n       )                                     ∂     y   sn         ∂     η   n         =       -     z     6      n              cos        (     α   +     γ   n     +     η   n       )                                     ∂     y   sn         ∂   α       =         -     z     6      n              cos        (     α   +     γ   n     +     η   n       )         -       c     1      n            cos        (     α   +     γ   n       )         -       b     2      n          sin                 α                                   ∂     y   sn         ∂   β       =         ∂     x   sn         ∂     z   0         =         ∂     y   sn         ∂     z   0         =   0                                   ∂     z   sn         ∂     z   0         =   1                               ∂     z   sn         ∂     z     6      n           =                  cos        (     α   +     γ   n     +     η   n       )          cos                 β             (   5.36   )                   ∂     z   sn         ∂     η   n         =                  -     z     6      n              sin        (     α   +     γ   n     +     η   n       )          cos                 β                                 ∂     z   sn         ∂   α       =                  {         -     z     6      n              sin        (     α   +     γ   n     +     η   n       )         -       c     1      n            sin        (     α   +     γ   n       )         +       b     2      n          cos                 α       }        cos                 β                                 ∂     z   sn         ∂   β       =                    -     {         z     6      n            cos        (     α   +     γ   n     +     η   n       )         +       c     1      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }          sin                 β     -       a     1      n          sin                 β                             ∴                                 T   sn   tr     =       1   2            m     s                 n            (         x   .       s                 n     2     +       y   .       s                 n     2     +       z   .       s                 n     2       )                     =       1   2          m     s                 n              ∑                 j   ,   k                         (           ∂     x     s                 n           ∂     q   j                ∂     x     s                 n           ∂     q   k                q   .     j            q   .     k       +         ∂     y     s                 n           ∂     q   j                ∂     y     s                 n           ∂     q   k                q   .     j            q   .     k       +         ∂     z     s                 n           ∂     q   j                ∂     z     s                 n           ∂     q   k                q   .     j            q   .     k         )                     (   5.37   )                     =                  1   2          m     s                 n            〈         z   .       6      n     2     +         η   .     n   2          z     6      n     2       +         α   .     2     [       z     6      n     2     +     c     1      n     2     +     b     2      n     2     +     2        {         z     6      n            c     1      n          cos                   η   n       -                                                      z     6      n            b     2      n            sin        (       γ   n     +     η   n       )         -       c     1      n            b     2      n          sin                   γ   n         }       ]     +         β   .     2     [     {     (         z     6      n            cos        (     α   +     γ   n     +     η   n       )         +                               (         (                      c     1      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       )       }     )     )     2     +     a     1      n     2       ]     +       z   .     0   2     +     2          z   .       6      n            α   .          {         c     1      n          sin                   η   n       +       b     2      n            cos        (       γ   n     +     η   n       )           }       -                              2          z   .       6      n            β   .          a     1      n            cos        (     α   +     γ   n     +     η   n       )         +     2          η   .     n          α   .          z     6      n            {       z     6      n       +       c     1      n          cos                   η   n       -       b     2      n            sin        (       γ   n     +     η   n       )           }       +                                2          η   .     n          β   .          z     6      n            a     1      n            sin        (     α   +     γ   n     +     η   n       )         +     2        α   .          β   .          a     1      n            {         z     6      n            sin        (     α   +     γ   n     +     η   n       )         +       c     1      n            sin        (     α   +     γ   n       )         -                                          b     2      n          cos                 α     }       +     2          z   .       6      n              z   .     0          cos        (     α   +     γ   n     +     η   n       )          cos                 β     -     2          η   .     n            z   .     0          z     6      n            sin        (     α   +     γ   n     +     η   n       )          cos                 β     +                              2        α   .            z   .     0          {         z     6      n            sin        (     α   +     γ   n     +     η   n       )         -       c     1      n            sin        (     α   +     γ   n       )         +       b     2      n          cos                 α       }        cos                 β     +                                2        β   .              z   .     0          [         {         z     6      n            cos        (     α   +     γ   n     +     η   n       )         +       c     1      n            sin        (     α   +     γ   n       )         +       b     2      n          cos                 α       }        sin                 β     +       α     1      n          cos                 β       ]         〉                   (   5.38   )                 T   sn   ro     ≅              0                                   U   sn     =                    m     s                 n          g                   z   sn       +       1   2              k     s                 n            (       z     6      n       -     l     s                 n         )       2                     =                  m     s                 n          g   [       z   0     +     {         z     6      n            cos        (     α   +     γ   n     +     η   n       )         +       c     1      n            cos        (     α   +     γ   n       )         +                                                b     2      n          sin                 α     }          cos                 β     -       a     1      n          sin                 β       ]     +       1   2              k     s                 n            (       z     6      n       -     l     s                 n         )       2                                       F   sn     =                  -     1   2            c   sn            z   .       6      n     2               (   5.39   )                   &lt;        Arm        &gt;                                            T   an   tr     =       1   2            m   an          (         x   .     an   2     +       y   .     an   2     +       z   .     an   2       )                 (   5.40   )             where                                 x   an     =                    {         e     1      n            sin        (     α   +     γ   n     +     θ   n       )         +       c     2      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }        sin                 β     +       a     1      n          cos                 β                     y   an     =                    e     1      n            cos        (     α   +     γ   n     +     θ   n       )         -       c     2      n            sin        (     α   +     γ   n       )         +       b     2      n          cos                 α                     z   an     =                  z   0     +       {         e     1      n            sin        (     α   +     γ   n     +     θ   n       )         +       c     2      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }        cos                 β     -       a     1      n          sin                 β                     (   5.41   )             and                             q     j   ,   k       =     θ   n       ,   α   ,   β   ,     z   0             (   5.42   )                   ∂     x   an         ∂     θ   n         =       e     1      n            cos        (     α   +     γ   n     +     θ   n       )          sin                 β                                 ∂     x   an         ∂   α       =       {         e     1      n            cos        (     α   +     γ   n     +     θ   n       )         -       c     2      n            sin        (     α   +     γ   n       )         +       b     2      n          cos                 α       }        sin                 β                                 ∂     x   an         ∂   β       =         {         e     1      n            sin        (     α   +     γ   n     +     θ   n       )         +       c     2      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }        cos                 β     -       a     1      n          sin                 β                                   ∂     y   an         ∂     θ   n         =       -     e     1      n              sin        (     α   +     γ   n     +     θ   n       )                                     ∂     y   an         ∂   α       =         -     e     1      n              sin        (     α   +     γ   n     +     θ   n       )         -       c     2      n            cos        (     α   +     γ   n       )         -       b     2      n          sin                 α                                   ∂     y   an         ∂   β       =         ∂     x   an         ∂     z   0         =         ∂     y   an         ∂     z   0         =   0                                   ∂     z   an         ∂     θ   n         =       e     1      n            cos        (     α   +     γ   n     +     θ   n       )          cos                 β                                 ∂     z   an         ∂   α       =       {         e     1      n            cos        (     α   +     γ   n     +     θ   n       )         -       c     2      n            sin        (     α   +     γ   n       )         +       b     2      n          cos                 α       }        cos                 β                                 ∂     z   an         ∂   β       =         -     {         e     1      n            sin        (     α   +     γ   n     +     θ   n       )         +       c     2      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }          sin                 β     -       a     1      n          cos                 β                                   ∂     z   an         ∂     z   0         =   1                         thus                                 T   an   tr     =       1   2            m   an          (         x   .     an   2     +       y   .     an   2     +       z   .     an   2       )                     =       1   2          m   an            ∑                 j   ,   k                         (           ∂     x   an         ∂     q   j                ∂     x   an         ∂     q   k                q   .     j            q   .     k       +         ∂     y   an         ∂     q   j                ∂     y   an         ∂     q   k                q   .     j            q   .     k       +         ∂     z   an         ∂     q   j                ∂     z   an         ∂     q   k                q   .     j            q   .     k         )                     (   5.43   )                     =                  1   2          m   an          〈           θ   .     n   2          e     1      n     2       +         α   .     2     [       e     1      n     2     +     c     2      n     2     +     b     2      n     2     -     2        {         e     1      n            c     2      n          sin                   θ   n       +       e     1      n            b     2      n            cos        (       γ   n     +     θ   n       )         +                                                    c     2      n            b     2      n          sin                   γ   n       }       ]     +         β   .     2     [         {         e     1      n            sin        (     α   +     γ   n     +     θ   n       )         +       c     2      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }     2     +                                    α     1      n     2     ]       +       z   .     0   2     +     2        θ   .          α   .          e     1      n            {       e     1      n       -       c     2      n          sin                   θ   n       +       b     2      n            cos        (       γ   n     +     θ   n       )           }       -                              2          θ   .     n          β   .          e     1      n            a     1      n            cos        (     α   +     γ   n     +     θ   n       )         -     2        α   .          β   .          a     1      n            {         e     1      n            cos        (     α   +     γ   n     +     θ   n       )         -                                            c     1      n            sin        (     α   +     γ   n       )         +       b     2      n          cos                 α       }       -     2          θ   .     n            z   .     0          e     1      n            cos        (     α   +     γ   n     +     θ   n       )          cos                 β     +                              2        α   .            z   .     0          {         e     1      n            cos        (     α   +     γ   n     +     θ   n       )         -       c     2      n            sin        (     α   +     γ   n       )         +       b     2      n          cos                 α       }        cos                 β     +                                2        β   .              z   .     0          [         {         e     1      n            sin        (     α   +     γ   n     +     θ   n       )         +       c     2      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }        sin                 β     +       α     1      n          cos                 β       ]         〉                   (   5.44   )                       T   an   ro     =       1   2          I   ax          ω   ax   2                   =       1   2              I   ax          (       α   .     +       θ   .     n       )       2                                             U   an     =       m   an          gz   an                   =       m   an          g        [       z   0     +       {         e     1      n            sin        (     α   +     γ   n     +     θ   n       )         +       c     2      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }        cos                 β     -       a     1      n          sin                 β       ]                       (   5.45   )                   &lt;        Wheel        &gt;                                            T   wn   tr     =       1   2            m   wn          (         x   .     wn   2     +       y   .     wn   2     +       z   .     wn   2       )                 (   5.46   )             where                                 x   wn     =         {         e     3      n            sin        (     α   +     γ   n     +     θ   n       )         +       c     2      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }        sin                 β     +       a     1      n          cos                 β                     y   wn     =         e     3      n            cos        (     α   +     γ   n     +     θ   n       )         -       c     2      n            sin        (     α   +     γ   n       )         +       b     2      n          cos                 α                     z   wn     =       z   0     +       {         e     3      n            sin        (     α   +     γ   n     +     θ   n       )         +       c     2      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }        cos                 β     -       a     1      n          sin                 β                     (   5.47   )                         
     Substituting m an  with m wn  and e 1n  with e 3n  in the equation for the arm, yields an equation for the wheel as:                      T   wn   tr     =                  1   2          m   wn          〈           θ   .     n   2          e     3      n     2       +         α   .     2     [       e     3      n     2     +     c     2      n     2     +     b     2      n     2     -     2        {         e     3      n            c     2      n          sin                   θ   n       +                                                      e     3      n            b     2      n            cos        (       γ   n     +     θ   n       )         +       c     2      n            b     2      n          sin                   γ   n         }       ]     +                                β   .     2     [     {         e     3      n            sin        (     α   +     γ   n     +     θ   n       )         +       c     2      n            cos        (     α   +     γ   n       )         +                                              +     b     2      n            sin                 α     }       2     +     a     1      n     2       ]     +       z   .     0   2     +     2        θ   .          α   .          e     3      n                                    {       e     3      n       -       c     2      n          sin                   θ   n       +       b     2      n            cos        (       γ   n     +     θ   n       )           }     -     2          θ   .     n          β   .          e     3      n            a     1      n          cos                                  (     α   +     γ   n     +     θ   n       )     -     2        α   .          β   .          a     1      n            {         e     3      n            cos        (     α   +     γ   n     +     θ   n       )         -                                            c     1      n            sin        (     α   +     γ   n       )         +       b     2      n          cos                 α       }       +                              2          θ   .     n            z   .     0          e     3      n            cos        (     α   +     γ   n     +     θ   n       )          cos                 β     +                              2        α   .            z   .     0          {         e     3      n            cos        (     α   +     γ   n     +     θ   n       )         -                                            c     2      n            sin        (     α   +     γ   n       )         +       b     2      n          cos                 α       }          cos                 β     -     2        β   .            z   .     0                                [     {         e     3      n            sin        (     α   +     γ   n     +     θ   n       )         +       c     2      n            sin        (     α   +     γ   n       )         +                                              b     2      n          sin                 α     }          sin                 β     +       α     1      n          cos                 β       ]     〉                 (   5.48   )                       T   wn   ro     =              0                 U   wn     =                    m   wn          gz   wn       +       1   2              k   wn          (       z     12      n       -     l   wn       )       2                     =                  m   wn        g   [       z   0     +     {         e     3      n            sin        (     α   +     γ   n     +     θ   n       )         +       c     2      n            cos        (     α   +     γ   n       )         +                                                b     2      n          sin                 α     }          cos                 β     -       a     1      n          sin                 β       ]     +       1   2              k   wn          (       z     12      n       -     l   wn       )       2                     F   wn     =                  -     1   2            c   wn            z   .       12      n     2                     (   5.49   )                 &lt;        Stabilizer        &gt;                               T   zn   tr     ≅   0           (   5.50   )                 T   zn   ro     ≅   0           (   5.51   )                       U     zi   ,   ii       ≅                  1   2              k   zi          (       z   zi     -     z   zii       )       2                   =                  1   2          k   zi     [       {         e     0      i            sin        (       γ   i     +     θ   i       )         +       c     2      i          cos                   γ   i         }     -                                    {         e     0      ii            sin        (       γ   ii     +     θ   ii       )         +       c     2      ii          cos                   γ   ii         }     ]       2               =                  1   2          k   zi          e     0      i     2            {       sin        (       γ   i     +     θ   i       )       +     sin        (       γ   ii     +     θ   ii       )         }     2                       where                                  e     0      ii         =     -     e     0      i           ,       c     2      ii       =     c     2      i         ,       γ   ii     =     -     γ   i                       U     ziii   ,   iv       ≅                  1   2              k   ziii          (       z   ziii     -     z   ziv       )       2                   =                  1   2            k   ziii     [       {         e     0      iii            sin        (       γ   iii     +     θ   iii       )         +       c     2      iii          cos                   γ   iii         }     -                                    {         e     0      iv            sin        (       γ   iv     +     θ   iv       )         +       c     2      iv          cos                   γ   iv         }     ]     2               =                  1   2          k   ziii          e     0      iii     2            {       sin        (       γ   iii     +     θ   iii       )       +     sin        (       γ   iv     +     θ   iiv       )         }     2                       where                   e     0      ii         =         -     e     0      iii                         c     2      iv         =     c     2      iii           ,       γ   iv     =     -     γ   iii                       (   5.52   )                 F   zn     ≅   0           (   5.53   )                         
     Therefore the total kinetic energy is:                T   tot     =       T   b   tr     +       ∑     n   =   i     iv                            T   sn   tr     +     T   an   tr     +     T   wn   tr     +     T   b   ro     +     T   an   ro                        (   5.54   )                       T   tot     =                  T   b   tr     +       ∑     n   =   i     iv                            T   sn   tr     +     T   an   tr     +     T   wn   tr     +     T   b   ro     +     T   an   ro                            =                  1   2          m   b          〈           α   .     2          (       b   0   2     +     c   0   2       )       +         β   .     2          {         (       a   0     +     a     1      i         )     2     +       (         b   0        sin                 α     +       c   0        cos                 α       )     2       }       +                                      z   .     0   2     -     2        α   .            β   .          (       a   0     +     a     1      i         )            (         b   0        cos                 α     -       c   0        sin                 α       )       -                                2        β   .            z   .     0          {         (       a   0     +     a     1      i         )        cos                 β     +       (         b   0        sin                 α     +       c   0        cos                 α       )        sin                 β       }       +                                  2        α   .              z   .     0          (         b   0        cos                 α     -       c   0        sin                 α       )          cos                 β     〉       +       ∑     n   =   i     iv                            1   2          m   sn          〈         z   .       6      n     2     +         η   .     n   2          z     6      n     2       +                                          α   .     2     [       z     6      n     2     +     c     1      n     2     +     b     2      n     2     +     2        {         z     6      n            c     1      n          cos                   η   n       -       z     6      n            b     2      n            sin        (       γ   n     +     η   n       )         -                                              c     1      n            b     2      n          sin                   γ   n       }       ]     +         β   .     2     [     {         z     6      n            cos        (     α   +     γ   n     +     η   n       )         +       c     1      n            cos        (     α   +     γ   n       )         +                                              b     2      n          sin                 α     }       2     +     a     1      n     2       ]     +       z   .     0   2     +     2          z   .       6      n            α   .          {         c     1      n          sin                   η   n       +       b     2      n            cos        (       γ   n     +     η   n       )           }       -                              2          z   .       6      n            β   .          a     1      n            cos        (     α   +     γ   n     +     η   n       )         +     2          η   .     n          α   .          z     6      n            {       z     6      n       +       c     1      n          cos                   η   n       -                                          b     2      n            sin        (       γ   n     +     η   n       )         }       +     2          η   .     n          β   .          z     6      n            a     1      n            sin        (     α   +     γ   n     +     η   n       )         +                              2        α   .          β   .          a     1      n            {         z     6      n            sin        (     α   +     γ   n     +     η   n       )         +       c     1      n            sin        (     α   +     γ   n       )         -       b     2      n          cos                 α       }       +                                2          z   .       6      n              z   .     0          cos        (     α   +     γ   n     +     η   n       )          cos                 β     -     2          η   .     n            z   .     0          z     6      n            sin        (     α   +     γ   n     +     η   n       )          cos                 β     +                                2        α   .            z   .     0          {         -     z     6      n              sin        (     α   +     γ   n     +     η   n       )         -       c     1      n            sin        (     α   +     γ   n       )         +       b     2      n          cos                 α       }        cos                 β     -                              2        β   .              z   .     0     [       {         z     6      n            cos        (     α   +     γ   n     +     η   n       )         -       c     1      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }     +                                          a     1      n          cos                 β     ]       〉     +       1   2          m   an          〈           θ   .     n   2          e     1      n     2       +         α   .     2          [     e     1      n     2     +     c     2      n     2     +     b     2      n     2     -     2        {         e     1      n            c     2      n          sin                   θ   n       +                                                    e     1      n            b     2      n            cos        (       γ   n     +     θ   n       )         +       c     2      n            b     2      n          sin                   γ   n         }     ]     +         β   .     2     [     {       e   i1          sin   (     α   +                                                    γ   n     +     θ   n       )     +       c     2      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }     2     +     a     1      n     2       ]     +       z   .     0   2     +                                  c     2      n          sin                   θ   n       +       b     2      n            cos        (       γ   n     +     θ   n       )           }     -     2          θ   .     n          β   .          e     1      n            a     1      n            cos   (     α   +                                      γ   n     +     θ   n       )     -     2        α   .          β   .          a     1      n            {         e     1      n            cos        (     α   +     γ   n     +     θ   n       )         -       c     1      n            sin        (     α   +     γ   n       )         +                                        b     2      n          cos                 α     }       +     2          θ   .     n            z   .     0          e     1      n            cos        (     α   +     γ   n     +     θ   n       )          cos                 β     +     2        α   .            z   .     0          {       e     1      n            cos   (     α   +                                          γ   n     +     θ   n       )     -       c     2      n            sin        (     α   +     γ   n       )         +         b     2      n          cos                 α     }   cos                 β     -     2        β   .              z   .     0     [     {       e     1      n            sin   (     α   +                                                γ   n     +     θ   n       )     +       c     2      n            cos        (     α   +     γ   n       )         +         b     2      n          sin                 α     }     +       a     1      n          cos                 β       〉     +                              1   2          m   wn          〈           θ   .     n   2          e     3      n     2       +         α   .     2     [       e     3      n     2     +     c     2      n     2     +     b     2      n     2     -     2        {         e     3      n            c     2      n          sin                   θ   n       -                                                      e     3      n            b     2      n            cos        (       γ   n     +     θ   n       )         +       c     2      n            b     2      n          sin                   γ   n         }       ]     +         β   .     2     [     {         e     3      n            sin        (     α   +     γ   n     +     θ   n       )         +                                                c     2      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }       2     +     a     1      n     2       ]     +       z   .     0   2     +     2        θ   .          α   .          e     3      n            {       e     3      n       -                                          c     2      n          sin                   θ   n       +       b     2      n            cos        (       γ   n     +     θ   n       )           }       -     2          θ   .     n          β   .          e     3      n            a     1      n            cos        (     α   +     γ   n     +     θ   n       )         -                              2        α   .          β   .          a     1      n            {         e     3      n            cos        (     α   +     γ   n     +     θ   n       )         -       c     1      n            sin        (     α   +     γ   n       )         +       b     2      n          cos                 α       }       +                                2          θ   .     n            z   .     0          e     3      n            cos        (     α   +     γ   n     +     η   n       )          cos                 β     +     2        α   .            z   .     0          {         e     3      n            cos        (     α   +     γ   n     +     θ   n       )         -                                              c     2      n            sin        (     α   +     γ   n       )         +       b     2      n          cos                 α       }          cos                 β     -     2        β   .              z   .     0     [     {         e     3      n            sin        (     α   +     γ   n     +     θ   n       )         -                                                c     2      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }       +       a     1      n          cos                 β       〉     +       1   2          (         I   bx            α   .     2       +       I   by            β   .     2         )       +                              1   2              I   anx          (       α   .     +       θ   .     n       )       2                        (   5.55   )                     =                  1   2     [           α   .     2          m   bbI       +         β   .     2          {       m   baI     +         m   b          (         b   0        sin                 α     +       c   0        cos                 α       )       2       }       +         z   .     0   2          m   b       -                                  2          α   .          (         β   .          m   ba       -         z   .     0          m   b        cos                 β       )            (         b   0        cos                 α     -       c   0        sin                 α       )       -     2        β   .            z   .     0          {         m   ba        cos                 β     +                                              m   b          (         b   0        sin                 α     +       c   0        cos                 α       )          sin                 β     }       ]     +       1   2            ∑     n   =   i     iv                              m   sn          (         z   .       6      n     2     +         η   .     n   2          z     6      n     2         )       +                                          θ   .     n   2          m   aw2In       +         z   .     0   2          m   sawn       +         α   .     2          〈       m   sawIn     +       m   sn          z     6      n       [       z     6      n       +     2        m   sn          {         c     1      n          cos                   η   n       -                                                          b     2      n            sin        (       γ   n     +     η   n       )         }       ]     -     2        m   aw1n          {         c     2      n          sin                   θ   n       -       b     2      n            cos        (       γ   n     +     θ   n       )           }         〉     +                                β   .     2          〈       m   saw2n     +       m   sn          {         z     6      n            cos        (     α   +     γ   n     +     η   n       )         +       c     1      n            cos        (     α   +     γ   n       )         +                                                b     2      n          sin                 α     }       2     +       m   an          {         e   1          sin        (     α   +     γ   n     +     θ   n       )         +       c     2      n            cos        (     α   +     γ   n       )         +                                          b     2      n          sin                 α     }       2     +       m   wn          {         e   3          sin        (     α   +     γ   n     +     θ   n       )         +       c     2      n            cos        (     α   +     γ   n       )         +                                            b     2      n          sin                 α     }       2     〉     +     2          z   .       6      n            α   .          m   sn          {         c     1      n          sin                   η   n       +       b     2      n            cos        (       γ   n     +     η   n       )           }       -                              2          z   .       6      n            β   .        m                   a     1      n            cos        (     α   +     γ   n     +     η   n       )         +     2          η   .     n          α   .          m   sn          z     6      n            {       z     6      n       +       c     1      n          cos                   η   n       -                                          b     2      n            sin        (       γ   n     +     η   n       )         }       +     2          η   .     n          β   .          m   sn          z     6      n            a     1      n            sin        (     α   +     γ   n     +     η   n       )         +                              2        θ   .            α   .          [       m   aw2In     -       m   aw1n          {         c     2      n          sin                   θ   n       -       b     2      n            cos        (       γ   n     +     θ   n       )           }         ]         -                                2        θ   .          β   .          m   aw1n          a     1      n            cos        (     α   +     γ   n     +     θ   n       )         +     2        α   .          β   .          a     1      n            {         m   sawcn          sin        (     α   +     γ   n       )         -                                            m   sawbn        cos                 α     +       m   sn          z     6      n            sin        (     α   +     γ   n     +     η   n       )         -       m   aw1n          cos        (     α   +     γ   n     +     θ   n       )           }       +                              2          z   .       6      n              z   .     0          m   sn          cos        (     α   +     γ   n     +     η   n       )          cos                 β     -     2        (       α   .     +       η   .     n       )            z   .     0          z     6      n            m   sn          sin   (     α   +                                          γ   n     +     η   n       )        cos                 β     +     2          θ   .     n            z   .     0          m   aw1n          cos        (     α   +     γ   n     +     θ   n       )          cos                 β     +                            2        α   .            z   .     0          {         m   aw1n          sin        (     α   +     γ   n     +     θ   n       )         -       m   sawcn          sin        (     α   +     γ   n       )         +                                        m   sawbn        cos                 α     }        cos                 β     -     2        β   .            z   .     0     [     {         z     6      n            m   sn          cos        (     α   +     γ   n     +     η   n       )         -       m   aw1n          sin   (     α   +                                          γ   n     )     +       m   sawcn          cos        (     α   +     γ   n       )         +         m   sawbn        sin                 α     }   sin                 β     +         m   sawan        cos                 β     ]   〉                      (   5.56   )                         
     where 
     
       
           m   ba   =m   b ( a   0   +a   1i ) 
       
     
     
       
           m   bbI   =m   b ( b   0   2   +c   0   2 )+ I   bx   
       
     
     
       
           m   baI   =m   b ( a   0   +a   1i ) 2   +I   by   
       
     
     
       
         
           m 
           sawn 
           =m 
           sn 
           +m 
           an 
           +m 
           wn 
         
       
     
     
       
           m   sawan =( m   sn   +m   an   +m   wn ) a   1n   
       
     
     
       
           m   sawbn =( m   sn   +m   an   +m   wn ) b   2n   
       
     
     
       
           m   sawcn   =m   sn   c   1n +( m   an   +m   wn ) c   2n   
       
     
     
       
           m   saw2n =( m   sn   +m   an   +m   wn ) a   1n   2   
       
     
     
       
           m   saw1n   =m   an   e   1n   2   +m   wn   e   3n   2   m   sn ( c   1n   2   +b   2n   2 −2 c   1n   b   2n  sin γ n )+( m   an   +m   wn )( c   2n   2   +b   2n   2 −2 c   2n   b   2n  sin γ n )+ I   axn   
       
     
     
       
         
           m 
           aw21n 
           =m 
           an 
           e 
           1n 
           2 
           +m 
           wn 
           e 
           3n 
           2 
           +I 
           axn 
         
       
     
     
       
         
           m 
           aw1n 
           =m 
           an 
           e 
           1n 
           +m 
           wn 
           e 
           3n 
         
       
     
     
       
           m   aw2n   =m   an   e   1n   2   +m   wn   e   3n   2   ( 5.57)   
       
     
     Hereafter variables and coefficients which have index “n” implies implicit or explicit that they require summation with n=i, ii, iii, and iv. 
     The total potential energy is:                U   tot     =       U   b     +       ∑     n   =   i     iv                            U   sn     +     U   an     +     U   wn     +     U   zn                        (   5.58   )                     =                    m   b        g        {       z   0     -       (       a   0     +     a     1      n         )        sin                 β     +       (         b   0        sin                 α     +       c   0        cos                 α       )        cos                 β       }       +                                ∑     n   =   i     iv                            m   sn          g   [       z   0     +     {         z     6      n            cos        (     α   +     γ   n     +     η   n       )         +       c     1      n            cos        (     α   +     γ   n       )         +                                                      b     2      n          sin                 α     }          cos                 β     -       a     1      n          sin                 β       ]     +       1   2              k   sn          (       z     6      n       -     l   sn       )       2       +                              m   an          g   [       z   0     +     {         e     1      n            sin        (     α   +     γ   n     +     θ   n       )         +       c     2      n            cos        (     α   +     γ   n       )         +                                                  b     2      n          sin                 α     }          cos                 β     -       a     1      n          sin                 β       ]     +       m   wn          g   [       z   0     +     {       e     3      n          sin                                              (     α   +     γ   n     +     θ   n       )     +       c     2      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }          cos                 β     -                                      a     1      n          sin                 β     ]       +       1   2              k   wn          (       z     12      n       -     l   wn       )       2              +       1   2          k   zi          e   oi   2          {       sin        (       γ   i     +     θ   i       )       +                                        sin        (       γ   i     +     θ   i       )       }       2     +       1   2          k   ziii          e   oiii   2            {       sin        (       γ   iii     +     θ   iii       )       +     sin        (       γ   iv     +     θ   iv       )         }     2                     (   5.59   )                     =                  g        {         z   0          m   b       -       m   ba        sin                 β     +         m   b          (         b   0        sin                 α     +       c   0        cos                 α       )          cos                 β       }       +                                ∑     n   =   i     iv                     〈     g   [     {         z   0          m   sawn       +       m   sn          z     6      n            cos        (     α   +     γ   n     +     η   n       )         +                                          m   aw1n          sin        (     α   +     γ   n     +     θ   n       )         +       m   sawcn          cos        (     α   +     γ   n       )         +                                          m   sawbn        sin                 α     }          cos                 β     -       m   sawan        sin                 β       ]     +       1   2              k   sn          (       z     6      n       -     l   sn       )       2       +                                1   2              k   wn          (       z     12      n       -     l   wn       )       2       〉     +       1   2          k   zi          e     0      i     2          {       sin        (       γ   i     +     θ   i       )       +                                        sin        (       γ   ii     +     θ   ii       )       }       2     +       1   2          k   ziii          e   oiii   2            {       sin        (       γ   iii     +     θ   iii       )       +     sin        (       γ   iv     +     θ   iv       )         }     2                     (   5.60   )                         
     where 
     
       
           m   ba   =m   b ( a   0   +a   1i ) 
       
     
     
       
           m   sawan =( m   sn   +m   an   +m   wn ) a   1n   
       
     
     
       
           m   sawbn =( m   sn   +m   an   +m   wn ) b   2n   
       
     
     
       
           m   sawcn   =m   sn   c   1n +( m   an   +m   wn ) c   2n   
       
     
     
       
         γ ii =−γ i   (5.61) 
       
     
     The Lagrangian is written as:                    L   =                  T   tot     -     U   tot                   =                  1   2     [           α   .     2          m   bbI       +         β   .     2          {       m   baI     +         m   b          (         b   0        sin                 α     +       c   0        cos                 α       )       2       }       +         z   .     0   2          m   b       -                                      (       2        α   .          β   .          m   ba       -         z   .     0          m   b        cos                 β       )          (         b   0        cos                 α     -       c   0        sin                 α       )       ]       -                                2        β   .            z   .     0          {         m   ba        cos                 β     +         m   b          (         b   0        sin                 α     +       c   0        cos                 α       )          sin                 β       }       ]       +                              1   2            ∑     n   =   i     iv                              m   sn          (         z   .       6      n     2     +         η   .     n   2          z     6      n     2         )       +         θ   .     n   2          m   aw2In       +         z   .     0   2          m   sawn       +                                        α   .     2          〈       m   sawIn     +       m   sn            z     6      n       [       z     6      n       +     2        {         c     1      n          cos                   η   n       -       b     2      n            sin   (       γ   n     +                                                              η   n     )     }     ]     -     2        m   aw1n          {         c     2      n          sin                   θ   n       -       b     2      n            cos        (       γ   n     +     θ   n       )           }         〉     +                                β   .     2          〈       m   saw2n     +       m   sn          {         z     6      n            cos        (     α   +     γ   n     +     η   n       )         +       c     1      n            cos        (     α   +     γ   n       )         +                                                b     2      n          sin                 α     }       2     +       m   an          {         e   1          sin        (     α   +     γ   n     +     θ   n       )         +       c     2      n            cos        (     α   +     γ   n       )         +                                          b     2      n          sin                 α     }       2     +       m   wn          {         e   3          sin        (     α   +     γ   n     +     θ   n       )         +       c     2      n            cos        (     α   +     γ   n       )         +                                            b     2      n          sin                 α     }       2     〉     +     2          z   .       6      n            α   .          m   sn          {         c     1      n          sin                   η   n       +       b     2      n            cos        (       γ   n     +     η   n       )           }       -                              2          z   .       6      n            β   .          m   sn          a     1      n            cos        (     α   +     γ   n     +     η   n       )         +     2          η   .     n          α   .          m   sn          z     6      n            {       z     6      n       +                                          c     1      n          cos                   η   n       -       b     2      n            sin        (       γ   n     +     η   n       )           }     +     2          η   .     n          β   .          m   sn          z     6      n            a     1      n            sin   (     α   +                                      γ   n     +     η   n       )     +     2        θ   .            α   .     [       m   aw2In     -       m   aw1n          {         c     2      n          sin                   θ   n       -                                                b     2      n            cos        (       γ   n     +     θ   n       )         }       ]     -     2        θ   .          β   .          m   aw1n          a     1      n            cos        (     α   +     γ   n     +     θ   n       )         +                            2        α   .          β   .          a     1      n            {         m   sawcn          sin        (     α   +     γ   n       )         -       m   sawbn        cos                 α     +       m   sn          z     6      n            sin   (     α   +                                                γ   n     +     η   n       )     -       m   aw1n          cos        (     α   +     γ   n     +     θ   n       )           }     +                            2          z   .     0          {           z   .       6      n            m   sn          cos        (     α   +     γ   n     +     η   n       )         +         (       α   .     +       θ   .     n         }          m   aw1n          cos   (     α   +                                            γ   n     +     θ   n       )     -       (       α   .     +       η   .     n       )          z     6      n            m   sn          sin        (     α   +     γ   n     +     η   n       )         -                                      α   .          m   sawcn          sin        (     α   +     γ   n       )         +       α   .          m   sawbn        cos                 α     -       β   .          m   sawcn         }          cos                 β     -                            2        β   .              z   .     0     [     {         z     6      n            m   sn          cos        (     α   +     γ   n     +     η   n       )         -       m   aw1n          sin        (     α   +     γ   n     +     θ   n       )         +                                                  m   sawcn          cos        (     α   +     γ   n       )         +       m   sawbn        sin                 α       }          sin                 β     }          -                              g        {         z   0          m   b       -       m   ba        sin                 β     +         m   b          (         b   0        sin                 α     +       c   0        cos                 α       )          cos                 β       }       -                                  1   2          k   zi          e     0      i     2            {       sin        (       γ   i     +     θ   i       )       +     sin        (       γ   ii     +     θ   ii       )         }     2       -       1   2          k   ziii          e     0      iii     2          {     sin   (       γ   iii     +                                              θ   iii     )     +     sin        (       γ   iv     +     θ   iv       )         }     2     -       ∑     n   =   i     iv                     〈     g   [         z   0          m   sawn       +                                    {         m   sn          z     6      n            cos        (     α   +     γ   n     +     η   n       )         +       m   aw1n          sin        (     α   +     γ   n     +     θ   n       )         +                                              m   sawcn          cos        (     α   +     γ   n       )         +       m   sawbn        sin                 α       }          cos                 β     -       m   sawan        sin                 β       ]     +                                1   2              k   sn          (       z     6      n       -     l   sn       )       2       +       1   2              k   wn          (       z     12      n       -     l   wn       )       2         〉                 (   5.62   )                         ∂   L       ∂     z   0         =                -     g        (       m   b     +     m   sawn       )                         ∂   L       ∂       z   .     0         =                      z   .     0          m   b       +       α   .          m   b        cos                   β        (         b   0        cos                 α     -       c   0        sin                 α       )         -       β   .          {         m   ba        cos                 β     +                                            m   b          (         b   0        sin                 α     +       c   0        cos                 α       )          sin                 β     }       +         z   .     0          m   sawn       +     {       z     6      n            m   sn          cos   (     α   +                                        γ   n     +     η   n       )     +       (       α   .     +       θ   .     n       )          m   aw1n          cos        (     α   +     γ   n     +     θ   n       )         -                                (       α   .     +       η   .     n       )          z     6      n            m   sn          sin        (     α   +     γ   n     +     θ   n       )         -       α   .          m   sawcn          sin   (     α   +                                            γ   n     )     +       α   .          m   sawbn        cos                 α     -       β   .          m   sawan         }        cos                 β     -       β   .          {       m   aw1n          sin   (     α   +                                          γ   n     +     θ   n       )     -       z     6      n            m   sn          cos        (     α   +     γ   n     +     η   n       )         +                                m   sawcn            cos        (     α   +     γ   n       )       ++          m   sawbn        sin                 α     }        sin                 β                           t            (       ∂   L       ∂       z   .     0         )       =                      z   ¨     0          (       m   b     +     m   sawn       )       +       α   ¨            m   b          (         b   0        cos                 α     -       c   0        sin                 α       )         -                                  β   .          α   .          m   b        sin                   β        (         b   0        cos                 α     -       c   0        sin                 α       )         +         α   .     2          m   b        cos                   β   (         b   0        sin                 α     +                                        c   0        cos                 α     )     -       β   ¨          {         m   ba        cos                 β     +                                          m   b          (         b   0        sin                 α     +       c   0        cos                 α       )          sin                 β     }       +                              β   .          {         β   .          m   ba        sin                 β     +       α   .            m   b          (         b   0        cos                 α     -       c   0        sin                 α       )          sin                 β     +                                        β   .            m   b          (         b   0        sin                 α     +       c   0        cos                 α       )          cos                 β     }       +     {         z   ¨       6      n            m   sn          cos   (     α   +                                        γ   n     +     η   n       )     -       (       α   .     +       η   .     n       )            z   .       6      n            m   sn          sin   (     α   +                                        γ   n     +     η   n       )     }     -       (       α   ¨     +       η   ¨     n       )          z     6      n            m   sn          sin   (     α   +                                      γ   n     +     η   n       )     -       (       α   .     +       η   .     n       )            z   .       6      n            m   sn          sin   (     α   +                                      γ   n     +     η   n       )     -         (       α   .     +       η   .     n       )     2          z     6      n            m   sn          cos   (     α   +                                      γ   n     +     η   n       )     -       α   ¨          m   sawcn          sin        (     α   +     γ   n       )         -                                  α   .     2          m   sawcn          sin        (     α   +     γ   n       )         +       α   ¨          m   sawbn        cos                 α     -                                          α   .     2          m   sawbn        sin                 α     -       β   ¨          m   sawan         }          cos                 β     -                              β   .          {           z   .       6      n            m   sn          cos        (     α   +     γ   n     +     η   n       )         -       (       α   .     +       θ   .     n       )          m   aw1n          cos   (     α   +                                            γ   n     +     θ   n       )     -       (       α   .     +       η   .     n       )          z     6      n            m   sn          sin        (     α   +     γ   n     +     η   n       )         -                                α   .          m   sawcn          sin        (     α   +     γ   n       )         -       α   .          m   sawbn        cos                 α     -                                      β   .          m   sawan       }          sin                 β     -       β   ¨          {         m   awln          sin        (     α   +     γ   n     +     θ   n       )         +                                      z     6      n            m   sn          cos        (     α   +     γ   n     +     η   n       )         +       m   awcn          cos        (     α   +     γ   n       )         +                                      m   sawbn        sin                 α     }          sin                 β     -       β   .          {       (       α   .     +       θ   .     n       )          m   awln          cos   (     α   +                                          γ   n     +     θ   n       )     +       z     6      n            m   sn          cos        (     α   +     γ   n     +     η   n       )         -                                (       α   .     +       η   .     n       )          z     6      n            m   sn          sin        (     α   +     γ   n     +     η   n       )         -                                        α   .          m   sawcn          sin        (     α   +     γ   n       )         +       α   .          m   sawbn        cos                 α       }          sin                 β     -                                β   .     2          {         m   aw1n          sin        (     α   +     γ   n     +     θ   n       )         -                                      z     6      n            m   sn          cos        (     α   +     γ   n     +     η   n       )         +                                    m   sawcn            cos        (     α   +     γ   n       )       ++          m   sawbn        sin                 α     }          cos                 β                                           ∂   L       ∂   β       =                    -     α   .              z   .     0          m   b        sin                   β        (         b   0        cos                 α     -       c   0        sin                 α       )         +       β   .            z   .     0          {         m   ba        sin                 β     -                                              m   b          (         b   0        sin                 α     -       c   0        cos                 α       )          cos                 β     }       )        g        {         m   ba        cos                 β     +                                        m   b          (         b   0        sin                 α     +       c   0        cos                 α       )          sin                 β     }       +     〈     g   [     {       m   sn          z     6      n            cos   (     α   +                                            γ   n     +     η   n       )     +       m   aw1n          sin        (     α   +     γ   n     +     θ   n       )         +                                      m   sawcn          cos        (     α   +     γ   n       )         +       m   sawbn        sin                 α       }          sin                 β     +                                  m   sawan        cos                 β     ]       -         z   .     0          {           z   .       6      n            m   sn          cos        (     α   +     γ   n     +     η   n       )         +                                      (       α   .     +       θ   .     n       )          m   aw1n          cos        (     α   +     γ   n     +     θ   n       )         -                                  (       α   .     +       η   .     n       )          z     6      n            m   sn          sin        (     α   +     γ   n     +     η   n       )         -       α   .          m   sawcn          sin   (     α   +                                            γ   n     )     +       α   .          m   sawbn        cos                 α     -       β   .          m   sawan         }        sin                 β     +                              β   .            z   .     0          {         m   aw1n          sin        (     α   +     γ   n     +     θ   n       )         +       z     6      n            m   sn          cos        (     α   +     γ   n     +     η   n       )         +                                            m   sawcn          cos        (     α   +     γ   n       )         +       m   sawbn        sin                 α       }          cos                 β     〉                 (   5.63   )                         ∂   L       ∂   α       =                    {           β   .     2            m   b          (         b   0        cos                 α     -       c   0        sin                 α       )         +       α   .          β   .          m   ba         }          (         b   0        sin                 α     +       c   0        cos                 α       )       -                                  α   .            z   .     0          m   b        cos                   β        (         b   0        sin                 α     +       c   0        cos                 α       )         -                                  β   .            z   .     0            m   b          (         b   0        cos                 α     -       c   0        sin                 α       )          sin                 β     +                                       β   .     2          〈       m   sn          {         z     6      n            cos        (     α   +     γ   n     +     η   n       )         +       c     1      n            cos        (     α   +     γ   n       )         +                                                b     2      n          sin                 α     }            {         -     z     6      n              sin        (     α   +     γ   n     +     η   n       )         -       c     1      n            sin        (     α   +     γ   n       )         +       b     2      n          cos                 α       }       +                              m   an          {         e     1      n            sin        (     α   +     γ   n     +     θ   n       )         +       c     2      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }          {       e   1          cos   (     α   +                                              γ   n     +     θ   n       )     -       c     2      n            sin        (     α   +     γ   n       )         +       b     2      n          cos                 α       }     +       m   wn          {       e     3      n            sin   (     α   +                                              γ   n     +     θ   n       )     +       c     2      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }          {       e   3          cos   (     α   +                                              γ   n     +     θ   n       )     -       c     2      n            sin        (     α   +     γ   n       )         +       b     2      n          cos                 α       }     〉     +                                  z   .       6      n            β   .          m   sn          a     1      n            sin        (     α   +     γ   n     +     η   n       )         +         η   .     n          β   .          m   sn          z     6      n            a     1      n            cos        (     α   +     γ   n     +     η   n       )         +                                  θ   .          β   .          m   aw1n          a     1      n            sin        (     α   +     γ   n     +     θ   n       )         +       α   .          β   .          a     1      n            {         m   sawcn          cos        (     α   +     γ   n       )         +                                        m   sawbn        sin                 α     +       m   sn          z     6      n            cos        (     α   +     γ   n     +     η   n       )         +       m   aw1n          sin   (     α   +                                        θ   n     )     }     -         z   .     0     (           z   .       6      n            m   sn          sin        (     α   +     γ   n     +     η   n       )         +       (       α   .     +       θ   .     n       )          m   aw1n          sin   (     α   +     γ   n     +                                          γ   n     +     θ   n       )     +       (       α   .     +       η   .     n       )          z     6      n            m   sn          cos        (     α   +     γ   n     +     η   n       )         +                                      α   .          m   sawcn          cos        (     α   +     γ   n       )         +       α   .          m   sawbn        sin                 α       }          cos                 β     -                              β   .              z   .     0     [     {         m   aw1n          cos        (     α   +     γ   n     +     θ   n       )         -       z     6      n            m   sn          sin        (     α   +     γ   n     +     η   n       )         -                                                m   sawcn          sin        (     α   +     γ   n       )         +       m   sawbn        cos                 α       }          sin                 β          -       gm   b     (         b   0        cos                 α     -                                      c   0        sin                 α     )        cos                 β     +     g        {         m   sn          z     6      n            sin        (     α   +     γ   n     +     η   n       )         -       m   aw1n          cos   (     α   +                                                γ   n     +     θ   n       )     +       m   sawcn          sin        (     α   +     γ   n       )         -       m   sawbn        cos                 α       }        cos                 β                 (   5.64   )                         ∂   L       ∂     η   n         =                      α   .     2          m   sn          z     6      n            {         -     c     1      n            sin                   η   n       -       b     2      n            cos        (       γ   n     +     η   n       )           }       +                                  β   .     2          m   sn          {         z     6      n            cos        (     α   +     γ   n     +     η   n       )         +                                          c     1      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }          {       -     z     6      n              sin        (     α   +     γ   n     +     η   n       )         }       +                                  z   .       6      n            α   .          m   sn          {         c     1      n          cos                   η   n       -       b     2      n            sin        (       γ   n     +     η   n       )           }       +                                    z   .       6      n            β   .          m   sn          a     1      n            sin        (     α   +     γ   n     +     η   n       )         -         η   .     n          α   .          m   sn          z     6      n            {         c     1      n          sin                   η   n       +                                          b     2      n            cos        (       γ   n     +     η   n       )         }       +         η   .     n          β   .          m   sn          z     6      n            a     1      n            cos        (     α   +     γ   n     +     η   n       )         +                                α   .          β   .          a     1      n            m   sn          z     6      n            cos        (     α   +     γ   n     +     η   n       )         +                                g                   m   sn          z     6      n            sin        (     α   +     γ   n     +     η   n       )          cos                 β     -                                  z   .     0          {           z   .       6      n            m   sn          sin        (     α   +     γ   n     +     η   n       )         +       (       α   .     +       η   .     n       )          z     6      n            m   sn          cos   (     α   +                                                γ   n     +     η   n       )     }        cos                 β     +       β   .            z   .     0          z     6      n            m   sn          sin        (     α   +     γ   n     +     η   n       )          sin                 β                   (   5.65   )                         ∂   L       ∂     θ   n         =                  -     k   zi            e     0      i     2          {       sin        (       γ   i     +     θ   i       )       +     sin        (       γ   ii     +     θ   ii       )         }          {       cos        (       γ   i     +     θ   i       )       +                                      cos        (       γ   ii     +     θ   ii       )       }       -       k   ziii          e     0      iii     2          {       sin        (       γ   iii     +     θ   iii       )       +                                    sin        (       γ   iv     +     θ   iv       )       }          {       cos        (       γ   iii     +     θ   iii       )       +                                  cos        (       γ   iv     +     θ   iv       )       }     -         α   .     2          m   aw1n          {         c     2      n          cos                   θ   n       +       b     2      n            sin   (       γ   n     +                                            θ   n     )     }     +         β   .     2          〈       m   an          {         e     1      n            sin        (     α   +     γ   n     +     θ   n       )         +       c     2      n            cos        (     α   +     γ   n       )         +                                              b     2      n          sin                 α     }            e     1      n            cos        (     α   +     γ   n     +     θ   n       )         +       m   wn          {         e     3      n            sin        (     α   +     γ   n     +     θ   n       )         +                                              c     2      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }            e     3      n            cos        (     α   +     γ   n     +     θ   n       )         〉     -                                θ   .          α   .          m   aw1n          {         c     2      n          cos                   θ   n       +       b     2      n            sin        (       γ   n     +     θ   n       )           }       +       θ   .          β   .          m   aw1n          a     1      n            sin   (     α   +                                        γ   n     +     θ   n       )     +       α   .          β   .          a     1      n            m   aw1n          sin        (     α   +     γ   n     +     θ   n       )         -       gm   aw1n          cos   (     α   +                                        γ   n     +     θ   n       )        cos                 β     -           z   .     0          (       α   .     +       θ   .     n       )            m   aw1n          sin        (     α   +     γ   n     +     θ   n       )          cos                 β     -                              β   .            z   .     0          m   aw1n          cos        (     α   +     γ   n     +     θ   n       )          sin                 β                   (   5.66   )                         ∂   L       ∂     z     6      n           =                    m   sn            η   .     n   2          z     6      n         +         α   .     2            m   sn          [       z     6      n       +     {         c     1      n          cos                   η   n       -       b     2      n            sin        (       γ   n     +     η   n       )           }       ]         +                                  β   .     2          m   sn          {         z     6      n            cos        (     α   +     γ   n     +     η   n       )         +       c     1      n            cos        (     α   +     γ   n       )         +                                        b     2      n          sin                 α     }          cos        (     α   +     γ   n     +     η   n       )         +                                  η   .     n          α   .          m   sn          {       2        z     6      n         +       c     1      n          cos                   η   n       -       b     2      n            sin        (       γ   n     +     η   n       )           }       +                                    η   .     n          β   .          m   sn          a     1      n            sin        (     α   +     γ   n     +     η   n       )         +       α   .          β   .          a     1      n            m   sn          sin        (     α   +     γ   n     +     η   n       )         -                                  gm   sn          cos        (     α   +     γ   n     +     η   n       )          cos                 β     -       k   sn          (       z     6      n       -     l   sn       )       -                                (       α   .     +       η   .     n       )            z   .     0          m   sn          sin   (     α   +                                        γ   n     +     η   n       )        cos                 β     -       β   .            z   .     0          m   sn          cos        (     α   +     γ   n     +     η   n       )          sin                 β                   (   5.67   )                                ∂   L       ∂     z     12      n           =     -       k   wn          (       z     12      n       -     l   wn       )                   (   5.68   )                         ∂   L       ∂     β   .         =                  β   .          〈       m   saw2n     +     m   baI     +         m   b          (         b   0        sin                 α     +       c   0        cos                 α       )       2     +                                    m   sn          {         z     6      n            cos        (     α   +     γ   n     +     η   n       )         +       c     1      n            cos        (     α   +     γ   n       )         +                                        b     2      n          sin                 α     }     2     +       m   an          {         e     1      n            sin        (     α   +     γ   n     +     θ   n       )         +                                          c     2      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }     2     +       m   wn          {       e     3      n            sin   (     α   +                                                  γ   n     +     θ   n       )     +       c     2      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }     2     〉     -       α   .            m   ba     (         b   0        cos                 α     -                                      c   0        sin                 α     )     -         z   .       6      n            m   sn          a     1      n            cos        (     α   +     γ   n     +     η   n       )         +                                  η   .     n          m   sn          z     6      n            a     1      n            sin        (     α   +     γ   n     +     η   n       )         -       θ   .          m   aw1n          a     1      n            cos        (     α   +     γ   n     +     θ   n       )         +                                α   .          a     1      n            {         m   sawcn          sin        (     α   +     γ   n       )         -       m   sawbn        cos                 α     +       m   sn          z     6      n            sin   (     α   +                                                γ   n     +     η   n       )     -       m   aw1n          cos        (     α   +     γ   n     +     θ   n       )           }     -         z   .     0     [     {         m   b          b   0        sin                 α     +                                        c   0        cos                 α     )       +       m   awln          sin        (     α   +     γ   n     +     η   n       )         +       z     6      n            m   sn          cos        (     α   +     γ   n     +     η   n       )         +                                        m   sawcn          cos        (     α   +     γ   n       )         +       m   sawbn        sin                 α       }          sin                 β     +       (       m   ba     +     m   sawcn       )        cos                 β       ]                 (   5.69   )                                 t            (       ∂   L       ∂     β   .         )       =                  β   ¨          〈       m   saw2n     +     m   baI     +         m   b          (         b   0        sin                 α     +       c   0        cos                 α       )       2     +                                    m   sn          {         z     6      n            cos        (     α   +     γ   n     +     η   n       )         +       c     1      n            cos        (     α   +     γ   n       )         +                                        b     2      n          sin                 α     }     2     +       m   an          {         e     1      n            sin        (     α   +     γ   n     +     θ   n       )         +                                          c     2      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }     2     +       m   wn          {       e     3      n            sin   (     α   +                                                  γ   n     +     θ   n       )     +       c     2      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }     2     〉     +                            2        β   .          〈         α   .            m   b          (         b   0        sin                 α     +       c   0        cos                 α       )            (         b   0        cos                 α     -       c   0        sin                 α       )       +                                    m   sn          {         z     6      n            cos        (     α   +     γ   n     +     η   n       )         +                                        c     1      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }          {         z   .       6      n            cos   (     α   +                                        γ   n     +     η   n       )     -       (       α   .     +       η   .     n       )          z     6      n            sin        (     α   +     γ   n     +     η   n       )         -       α   .     [       c     1      n            sin   (     α   +                                            γ   n     )     -       b     2      n          cos                 α       ]     }     +       m   an          {         e     1      n            sin        (     α   +     γ   n     +     θ   n       )         +                                          c     2      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }            {         (       α   .     +       θ   .     n       )          e     1      n            cos        (     α   +     γ   n     +     θ   n       )         -                                      α   .          [         c     2      n            sin        (     α   +     γ   n       )         -       b     2      n          cos                 α       ]       }       +       m   wn          {       e     3      n            sin   (     α   +                                              γ   n     +     θ   n       )     +       c     2      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }          {       (       α   .     +       θ   .     n       )          e     3      n            sin   (     α   +                                              γ   n     +     θ   n       )     -       α   .          [         c     2      n            sin        (     α   +     γ   n       )         -       b     2      n          cos                 α       ]         }     〉     -                                α   ¨            m   ba          (         b   0        cos                 α     -       c   0        sin                 α       )         +         α   .     2            m   ba          (         b   0        sin                 α     +       c   0        cos                 α       )         -                                    z   ¨       6      n            m   sn          a     1      n            cos        (     α   +     γ   n     +     η   n       )         +           z   .       6      n            (       α   .     +       η   .     n       )            m   sn          a     1      n            sin   (     α   +                                        γ   n     +     η   n       )     +         η   ¨     n          m   sn          z     6      n            a     1      n            sin        (     α   +     γ   n     +     η   n       )         +                                  η   .     n          m   sn            z   .       6      n            a     1      n            sin        (     α   +     γ   n     +     η   n       )         +                                    η   .     n          (       α   .     +       η   .     n       )            m   sn          z     6      n            a     1      n            cos   (     α   +                                      γ   n     +     η   n       )     -         θ   ¨     n          m   aw1n          a     1      n            cos        (     α   +     γ   n     +     θ   n       )         +                                    θ   .     n          (       α   .     +       θ   .     n       )            m   aw1n          a     1      n            sin        (     α   +     γ   n     +     θ   n       )         +       α   ¨          a     1      n            {       m   sawcn          sin   (     α   +                                          γ   n     )     -       m   sawbn        cos                 α     +       m   sn          z     6      n            sin        (     α   +     γ   n     +     η   n       )         -                                  m   aw1n          cos        (     α   +     γ   n     +     θ   n       )         }       +       α   .          a     1      n            {         α   .          m   sawcn          cos        (     α   +     γ   n       )         +                                      α   .          m   sawbn        sin                 α     +       (       α   .     +       η   .     n       )          m   sn          z     6      n            cos        (     α   +     γ   n     +     η   n       )         +                                  m   sn            z   .       6      n            sin        (     α   +     γ   n     +     η   n       )         +       (       α   .     +       θ   .     n       )          m   aw1n          sin   (     α   +                                          γ   n     +     θ   n       )     }     -         z   ¨     0     [     {         m   b          (         b   0        sin                 α     +       c   0        cos                 α       )       +       m   awln          sin   (     α   +                                            γ   n     +     θ   n       )     +       z     6      n            m   sn          cos        (     α   +     γ   n     +     η   n       )         +       m   sawcn          cos   (     α   +                                              γ   n     )     +       m   sawbn        sin                 α       }        sin                 β     +     (       m   ba     +       m   sawan        cos                 β           ]     -                                z   .     0     [     {         α   .            m   b          (         b   0        cos                 α     -       c   0        sin                 α       )         +       (       α   .     +       θ   .     n       )          m   aw1n          cos   (     α   +                                            γ   n     +     θ   n       )     +         z   .       6      n              m   sn          (     α   +     γ   n     +     η   n       )         -       (       α   .     +       η   .     n       )          z     6      n            m   sn          sin   (     α   +                                            γ   n     +     η   n       )     -       α   .          m   sawcn          sin        (     α   +     γ   n       )         +       α   .          m   sawbn        cos                 α       }        sin                 β     +                              β   .          {         m   b          (         b   0        sin                 α     +       c   0        cos                 α       )       +       m   aw1n          sin        (     α   +     γ   n     +     θ   n       )         +                                      z     6      n            m   sn          cos        (     α   +     γ   n     +     η   n       )         +       m   sawcn          cos        (     α   +     γ   n       )         +                                            m   sawbn        sin                 α     }        cos                 β     -     β   .       .          (       m   ba     +     m   sawan       )          sin                 β     ]                 (   5.70   )                         ∂   L       ∂     α   .         =                    α   .          m   bbI       -       β   .            m   ba          (         b   0        cos                 α     -       c   0        sin                 α       )         +                                    z   .     0          m   b        cos                   β        (         b   0        cos                 α     -       c   0        sin                 α       )         +                                α   .          〈       m   sawIn     +       m   sn            z     6      n       [       z     6      n       +     2        {         c     1      n          cos                   η   n       -                                                          b     2      n            sin        (       γ   n     +     η   n       )         }       ]     -     2        m   aw1n          {         c     2      n          sin                   θ   n       -       b     2      n            cos        (       γ   n     +     θ   n       )           }         〉     +                                  z   .       6      n            m   sn          {         c     1      n          sin                   η   n       +       b     2      n            cos        (       γ   n     +     η   n       )           }       +         η   .     n          m   sn          z     6      n            {       z     6      n       +                                            c     1      n          cos                   η   n       -       b     2      n            sin        (       γ   n     +     η   n       )           }       +       θ   .     [       m   aw2In     -       m   aw1n          {         c     2      n          sin                   θ   n       -                                              b     2      n            cos        (       γ   n     +     θ   n       )         }       ]     +       β   .          a     1      n            {         m   sawcn          sin        (     α   +     γ   n       )         -       m   sawbn        cos                 α     +                                          m   sn          z     6      n            sin        (     α   +     γ   n     +     η   n       )         -       m   aw1n          cos        (     α   +     γ   n     +     θ   n       )           }       +                                z   .     0          {         m   aw1n          cos        (     α   +     γ   n     +     θ   n       )         -       z     6      n            m   sn          sin        (     α   +     γ   n     +     η   n       )         -                                          m   sawcn          sin        (     α   +     γ   n       )         +       m   sawbn        cos                 α       }          cos                 β                 (   5.71   )                                 t            (       ∂   L       ∂     α   .         )       =                    -     β   ¨              m   ba          (         b   0        cos                 α     -       c   0        sin                 α       )         +       β   .          α   .            m   ba          (         b   0        sin                 α     +       c   0        cos                 α       )         +                                    z   ¨     0          m   b        cos                   β        (         b   0        cos                 α     -       c   0        sin                 α       )         -       β   .            z   .     0          m   b        sin                   β   (         b   0        cos                 α     -                                          c   0        sin                 α     )       -       α   .            z   .     0          m   b        cos                   β        (         b   0        sin                 α     +       c   0        cos                 α       )         +       α   ¨          〈       m   bbI     +                                    m   sawIn     +       m   sn            z     6      n            [       z     6      n       +     2        {         c     1      n          cos                   η   n       -       b     2      n            sin        (       γ   n     +     η   n       )           }         ]         -                                  2        m   aw1n          {         c     2      n          sin                   θ   n       -       b     2      n            cos        (       γ   n     +     θ   n       )           }       〉       +       α   .          〈       m   sn              z   .       6      n       [       z     6      n       +                                          2        {         c     1      n          cos                   η   n       -       b     2      n            sin        (       γ   n     +     η   n       )           }       ]       +       m   sn            z     6      n       [         z   .       6      n       -                                      2          η   .     n          {         c     1      n          sin                   η   n       +       b     2      n            cos        (       γ   n     +     η   n       )           }       ]       -     2          θ   .     n          m   aw1n          {         c     2      n          cos                   θ   n       +                                          b     2      n            sin        (       γ   n     +     θ   n       )         }       〉     +         z   ¨       6      n            m   sn          {         c     1      n          sin                   η   n       +       b     2      n            cos        (       γ   n     +     η   n       )           }       +                                  z   .       6      n              η   .     n          m   sn          {         c     1      n          cos                   η   n       -       b     2      n            sin        (       γ   n     +     η   n       )           }       +         η   ¨     n          m   sn          z     6      n            {       z     6      n       +                                            c     1      n          cos                   η   n       -       b     2      n            sin        (       γ   n     +     η   n       )           }       +         η   .     n          m   sn            z   .       6      n            {       z     6      n       +       c     1      n          cos                   η   n       -                                        b     2      n            sin        (       γ   n     +     η   n       )         }       +         η   .     n          m   sn          z     6      n            {         z   .       6      n       -         η   .     n     [         c     1      n          sin                   η   n       +       b     2      n          cos                                              (       γ   n     +     η   n       )     ]       }     +       θ   ¨     [       m   aw2In     -       m   aw1n          {         c     2      n          sin                   θ   n       -       b     2      n            cos   (       γ   n     +                                                      θ   n     )     }     ]     -         θ   .     n   2          m   aw1n          {         c     2      n          cos                   θ   n       +       b     2      n            sin        (       γ   n     +     θ   n       )           }         ]     +                              β   ¨          a     1      n            {         m   sawcn          sin        (     α   +     γ   n       )         -       m   sawbn        cos                 α     +       m   sn          z     6      n            sin   (     α   +                                                γ   n     +     η   n       )     -       m   aw1n          cos        (     α   +     γ   n     +     θ   n       )           }     +                              β   .          a     1      n            {       α   .     [         m   sawcn          cos        (     α   +     γ   n       )         +                                        m   sawbn        sin                 α     ]     +       m   sn            z   .       6      n            sin        (     α   +     γ   n     +     η   n       )         +                                (       α   .     +       η   .     n       )          m   sn          z     6      n            cos        (     α   +     γ   n     +     η   n       )         +       (       α   .     +       θ   .     n       )          m   aw1n          sin   (     α   +                                          γ   n     +     θ   n       )     }     -         z   ¨     0          {         m   aw1n          cos        (     α   +     γ   n     +     θ   n       )         +                                      z     6      n            m   sn          sin        (     α   +     γ   n     +     η   n       )         -       m   sawcn          sin        (     α   +     γ   n       )         +                                      m   sawbn        cos                 α     }          cos                 β     -         z   .     0          {         -     (       α   .     +       θ   .     n       )            m   aw1n          sin        (     α   +     γ   n     +     θ   n       )         +                                        z   .       6      n            m   sn          sin        (     α   +     γ   n     +     η   n       )         -       (       α   .     +       η   .     n       )          z     6      n            m   sn          cos   (     α   +                                              γ   n     +     η   n       )     -       α   .          m   sawcn          cos        (     α   +     γ   n       )         -       α   .          m   sawbn        sin                 α       }        cos                 β     -                              β   .            z   .     0          {         m   aw1n          cos        (     α   +     γ   n     +     θ   n       )         -       z     6      n            m   sn          sin   (     α   +                                                γ   n     +     η   n       )     -       m   sawcn          sin        (     α   +     γ   n       )         +       m   sawbn        cos                 α       }        sin                 β                 (   5.72   )                         ∂   L       ∂       η   .     n         =                    m   sn            η   .     n          z     6      n     2       +       α   .          m   sn          z     6      n            {       z     6      n       +       c     1      n          cos                   η   n       -       b     2      n            sin        (       γ   n     +     η   n       )           }       +                                  β   .          m   sn          z     6      n            a     1      n            sin        (     α   +     γ   n     +     η   n       )         -         z   .     0          z     6      n            m   sn          sin        (     α   +     γ   n     +     η   n       )          cos                 β                     (   5.73   )                                 t            (       ∂   L       ∂       η   .     n         )       =                    m   sn            η   ¨     n          z     6      n     2       +     2        m   sn            η   .     n            z   .       6      n            z     6      n         +       α   ¨          m   sn          z     6      n            {       z     6      n       +       c     1      n          cos                   η   n       -                                          b     2      n            sin        (       γ   n     +     η   n       )         }       +       α   .          m   sn            z   .       6      n            {       z     6      n       +       c     1      n          cos                   η   n       -                                        b     2      n            sin        (       γ   n     +     η   n       )         }       +       α   .          m   sn          z     6      n            {         z   .       6      n       -         η   .     n     [         c     1      n          sin                   η   n       +                                              b     2      n            cos        (       γ   n     +     η   n       )         ]       }     +       β   ¨          m   sn          z     6      n            a     1      n            sin        (     α   +     γ   n     +     η   n       )         +                                β   .          m   sn            z   .       6      n            a     1      n            sin        (     α   +     γ   n     +     η   n       )         +                                    β   .          (       α   .     +       η   .     n       )            m   sn          z     6      n            a     1      n            cos        (     α   +     γ   n     +     η   n       )         -                                    z   ¨     0          z     6      n            m   sn          sin        (     α   +     γ   n     +     η   n       )          cos                 β     -         z   .     0          z     6      n            m   sn          sin   (     α   +                                          γ   n     +     η   n       )        cos                 β     -       (       α   .     +       η   .     n       )            z   .     0          z     6      n            m   sn          cos   (     α   +                                        γ   n     +     η   n       )        cos                 β     -       β   .            z   .     0          z     6      n            m   sn          sin        (     α   +     γ   n     +     η   n       )          cos                 β                   (   5.74   )                         ∂   L       ∂       θ   .     n         =                      θ   .     n          m   aw2In       +       α   .          [       m   aw2In     -       m   aw1n          {         c     2      n          sin                   θ   n       -       b     2      n            cos        (       γ   n     +     θ   n       )           }         ]       -                                  β   .          m   aw1n          a     1      n            cos        (     α   +     γ   n     +     θ   n       )         +         z   .     0          m   aw1n          cos        (     α   +     γ   n     +     θ   n       )          cos                 β                     (   5.75   )                                 t            (       ∂   L       ∂       θ   .     n         )       =                      θ   ¨     n          m   aw2In       +       α   ¨     [       m   aw2In     -       m   aw1n          {         c     2      n          sin                   θ   n       -       b     2      n            cos   (       γ   n     +                                                    θ   n     )     }     ]     -       α   .            θ   .     n          m   aw1n          {         c     2      n          cos                   θ   n       +       b     2      n            sin        (       γ   n     +     θ   n       )           }       -                                β   ¨          m   aw1n          a     1      n            cos        (     α   +     γ   n     +     θ   n       )         +                                    β   .          (       α   .     +       θ   .     n       )            m   aw1n          a     1      n            sin        (       γ   n     +     θ   n       )         +                                    z   ¨     0          m   aw1n          cos        (     α   +     γ   n     +     θ   n       )          cos                 β     -                                  (       α   .     +       θ   .     n       )            z   .     0          m   aw1n          sin        (     α   +     γ   n     +     θ   n       )          cos                 β     -                                β   .            z   .     0          m   aw1n          cos        (     α   +     γ   n     +     θ   n       )          sin                 β                   (   5.76   )                         ∂   L       ∂       z   .       6      n           =                    m   sn            z   .       6      n         +       α   .          m   sn          {         c     1      n          sin                   η   n       +       b     2      n            cos        (       γ   n     +     η   n       )           }       -                                  β   .          m   sn          a     1      n            cos        (     α   +     γ   n     +     η   n       )         +         z   .     0          m   sn          cos        (     α   +     γ   n     +     η   n       )          cos                 β                     (   5.77   )                                 t            (       ∂   L       ∂       z   .       6      n           )       =                    m   sn            z   ¨       6      n         +       α   ¨          m   sn          {         c     1      n          sin                   η   n       +       b     2      n            cos        (       γ   n     +     η   n       )           }       +                                  α   .            η   .     n          m   sn          {         c     1      n          cos                   η   n       -       b     2      n            sin        (       γ   n     +     η   n       )           }       -       β   ¨          m   sn          a     1      n            cos   (     α   +                                        γ   n     +     η   n       )     +         β   .          (       α   .     +       η   .     n       )            m   sn          a     1      n            sin        (     α   +     γ   n     +     η   n       )         +                                  z   ¨     0          m   sn          cos        (     α   +     γ   n     +     η   n       )          cos                 β     -       (       α   .     +       η   .     n       )            z   .     0          m   sn          sin   (     α   +                                          γ   n     +     η   n       )        cos                 β     -       β   .            z   .     0          m   sn          cos        (     α   +     γ   n     +     η   n       )          sin                 β                   (   5.78   )                                ∂   L       ∂       z   .       12      n           =   0             (   5.79   )                                        t            (       ∂   L       ∂       z   .       12      n           )       =   0             (   5.80   )                         
     The dissipative function is:                F   tot     =       -     1   2            (         c   sn            z   .       6      n     2       +       c   wn            z   .       12      n     2         )               (   5.81   )                         
     The constraints are based on geometrical constraints, and the touch point of the road and the wheel. The geometrical constraint is expressed as 
     
       
           e   2n  cos θ n =−( z   6n   −d   1n )sin η n   
       
     
     
       
           e   2n  sin θ n −( z   6n   −d   1n )cos η n   =c   1n   −c   2n   (5.82) 
       
     
     The touch point of the road and the wheel is defined as                      z   tn     =                z     P     touchpoint                 n     r                   =                  z   0     +     {         z     12      n          cos                 α     +       e     3      n            sin        (     α   +     γ   n     +     θ   n       )         +       c     2      n            cos        (     α   +     γ   n       )         +                                          b     2      n          sin                 α     }          cos                 β     -       a     1      n          sin                 β                 =                  R   n          (   t   )                     (   5.83   )                         
     where R n (t) is road input at each wheel. 
     Differentials are: 
     
       
         {dot over (θ)} n   e   2n  sin θ n   −{dot over (z)}   6n  sin η n −{dot over (η)} n ( z   6n   −d   1n )cos η n =0 
       
     
     
       
         {dot over (θ)} n   e   2n  cos θ n   −{dot over (z)}   6n  cos η n +{dot over (η)} n ( z   6n   −d   1n )sin η n =0 
       
       
         
           
             
               
                 
                   
                     
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                   ( 
                   5.84 
                   ) 
                 
               
             
           
         
         
         
             
         
       
     
     Since the differentials of these constraints are written as                    ∑   j            a     l                 n                 j          d                     q   .     j         +       a                  l                 n                 t                 t         =     0                   (       l   =   1     ,   2   ,       3                 n     =   i     ,   ii   ,   iii   ,   iv     )               (   5.85   )                         
     then the values a 1nj  are obtained as follows. 
     a 1n0 =0 
     a 2n0 =0 
     a 3n0 =1 
     
       
           a   1n1 =0 , a   1n2 =0 , a   1n3 =−( z   6n   −d   1n )cos η n   , a   1n4   =e   2n  sin θ n   , a   1n5 =−sin η n   , a   1n6 =0 
       
     
     
       
           a   2n1 =0 , a   2n2 =0 , a   2n3 =( z   6n   −d   1n )sin η n   , a   2n4   =e   2n  cos θ n   , a   2n5 =−cos η n   , a   2n6 =0 
       
     
     
       
           a   3n1   =−{z   12n  cos α+ e   3n  sin(α+γ n +θ n )+ c   2n  cos(α+γ n )+ b   2n  sin α} sin β+a 1n  cos β, 
       
     
     
       
           a   3n2   ={−z   12n  sin α+ e   3n  cos(α+γ n θ n )− c   2n  sin(α+γ n )+ b   2n  cos α} cos β, 
       
     
     
       
           a   3n3 =0,  a   3n4   =e   3n  cos(α+γ n +θ n ) cos β,  a   3n5 =0,  a   3n6  =cos α cos β  (5.86) 
       
     
     From the above, Lagrange&#39;s equation becomes                            t            (       ∂   L       ∂       q   .     j         )       -       ∂   L       ∂     q   j           =       Q   j     +       ∑     l   ,   n              λ     l                 n            a     l                 n                 j                     (   5.87   )                         
     where 
     
       
         
           q 
           0 
           =z 
           0 
         
       
     
     
       
         
           q 
           1 
           =β, q 
           2 
           =α, q 
           3i 
           =η 
           i 
           , q 
           4i 
           =θ 
           i 
           , q 
           5i 
           =z 
           6i 
           , q 
           6i 
           =z 
           12i 
         
       
     
     
       
         
           q 
           3ii 
           =η 
           ii 
           , q 
           4ii 
           =θ 
           ii 
           , q 
           5ii 
           =z 
           6ii 
           , q 
           6ii 
           =z 
           12ii 
         
       
     
     
       
         
           q 
           3iii 
           =η 
           iii 
           , q 
           4iii 
           =θ 
           iii 
           , q 
           5iii 
           =z 
           6iii 
           , q 
           6iii 
           =z 
           12iii 
         
       
     
     
       
           q   3iv   =η   iv   , q   4iv   =θ   iv   , q   5iv   =z   6iv   , q   6iv   =z   12iv   (5.88) 
       
     
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                              
                             
                                
                               t 
                             
                           
                            
                           
                             ( 
                             
                               
                                 ∂ 
                                 L 
                               
                               
                                 ∂ 
                                 
                                   
                                     z 
                                     . 
                                   
                                   0 
                                 
                               
                             
                             ) 
                           
                         
                         - 
                         
                           
                             ∂ 
                             L 
                           
                           
                             ∂ 
                             
                               z 
                               0 
                             
                           
                         
                       
                       = 
                       
                         
                           
                             
                               ∂ 
                               F 
                             
                             
                               ∂ 
                               
                                 
                                   z 
                                   . 
                                 
                                 0 
                               
                             
                           
                           + 
                           
                             
                               ∑ 
                               
                                 l 
                                 , 
                                 n 
                               
                             
                              
                             
                               
                                 λ 
                                 
                                   l 
                                    
                                   
                                       
                                   
                                    
                                   n 
                                 
                               
                                
                               
                                 a 
                                 
                                   
                                       
                                   
                                    
                                   
                                     l 
                                      
                                     
                                         
                                     
                                      
                                     n 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                 
                               
                                
                               
                                   
                               
                                
                               l 
                             
                           
                         
                         = 
                         1 
                       
                     
                     , 
                     2 
                     , 
                     
                       
                         3 
                          
                         
                             
                         
                          
                         n 
                       
                       = 
                       i 
                     
                     , 
                     ii 
                     , 
                     iii 
                     , 
                     iv 
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         
                           z 
                           ¨ 
                         
                         0 
                       
                        
                       
                         ( 
                         
                           
                             m 
                             b 
                           
                           + 
                           
                             m 
                             sawn 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       
                         α 
                         ¨ 
                       
                        
                       
                         m 
                         b 
                       
                        
                       cos 
                        
                       
                           
                       
                        
                       
                         β 
                          
                         
                           ( 
                           
                             
                               
                                 b 
                                 0 
                               
                                
                               cos 
                                
                               
                                   
                               
                                
                               α 
                             
                             - 
                             
                               
                                 c 
                                 0 
                               
                                
                               sin 
                                
                               
                                   
                               
                                
                               α 
                             
                           
                           ) 
                         
                       
                     
                     - 
                     
                       
                         
                           α 
                           . 
                         
                         2 
                       
                        
                       
                         m 
                         b 
                       
                        
                       cos 
                        
                       
                           
                       
                        
                       
                         β 
                          
                         
                           ( 
                           
                             
                               
                                 b 
                                 0 
                               
                                
                               sin 
                                
                               
                                   
                               
                                
                               α 
                             
                             - 
                             
                               
                                 c 
                                 0 
                               
                                
                               cos 
                                
                               
                                   
                               
                                
                               α 
                             
                           
                           ) 
                         
                       
                     
                     - 
                     
                       
                         β 
                         ¨ 
                       
                        
                       
                         { 
                         
                           
                             
                               m 
                               ba 
                             
                              
                             cos 
                              
                             
                                 
                             
                              
                             β 
                           
                            
                           
                               
                           
                           + 
                           
                             
                               
                                 m 
                                 b 
                               
                                
                               
                                 ( 
                                 
                                   
                                     
                                       b 
                                       0 
                                     
                                      
                                     sin 
                                      
                                     
                                         
                                     
                                      
                                     α 
                                   
                                   - 
                                   
                                     
                                       c 
                                       0 
                                     
                                      
                                     cos 
                                      
                                     
                                         
                                     
                                      
                                     α 
                                   
                                 
                                 ) 
                               
                             
                              
                             sin 
                              
                             
                                 
                             
                              
                             β 
                           
                         
                         } 
                       
                     
                     + 
                     
                       
                         β 
                         . 
                       
                        
                       
                         { 
                         
                           
                             
                               
                                 β 
                                 . 
                               
                                
                               
                                 ( 
                                 
                                   
                                     m 
                                     ba 
                                   
                                   + 
                                   
                                     m 
                                     sawan 
                                   
                                 
                                 ) 
                               
                             
                              
                             sin 
                              
                             
                                 
                             
                              
                             β 
                           
                           + 
                           
                             
                               β 
                               . 
                             
                              
                             
                               
                                 m 
                                 b 
                               
                                
                               
                                 ( 
                                 
                                   
                                     
                                       b 
                                       0 
                                     
                                      
                                     sin 
                                      
                                     
                                         
                                     
                                      
                                     α 
                                   
                                   - 
                                   
                                     
                                       c 
                                       0 
                                     
                                      
                                     cos 
                                      
                                     
                                         
                                     
                                      
                                     α 
                                   
                                 
                                 ) 
                               
                             
                              
                             cos 
                              
                             
                                 
                             
                              
                             β 
                           
                         
                         } 
                       
                     
                     + 
                     
                       
                         
                           
                             
                               { 
                               
                                 
                                   
                                     
                                       z 
                                       ¨ 
                                     
                                     
                                       6 
                                        
                                       n 
                                     
                                   
                                    
                                   
                                     m 
                                     sn 
                                   
                                    
                                   
                                     cos 
                                      
                                     
                                       ( 
                                       
                                         α 
                                         + 
                                         
                                           γ 
                                           n 
                                         
                                         + 
                                         
                                           η 
                                           n 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                 - 
                                 
                                   2 
                                    
                                   
                                     ( 
                                     
                                       
                                         α 
                                         . 
                                       
                                       + 
                                       
                                         
                                           η 
                                           . 
                                         
                                         n 
                                       
                                     
                                     ) 
                                   
                                    
                                   
                                     
                                       z 
                                       . 
                                     
                                     
                                       6 
                                        
                                       n 
                                     
                                   
                                    
                                   
                                     m 
                                     sn 
                                   
                                    
                                   
                                     sin 
                                      
                                     
                                       ( 
                                       
                                         α 
                                         + 
                                         
                                           γ 
                                           n 
                                         
                                         + 
                                         
                                           η 
                                           n 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     ( 
                                     
                                       
                                         α 
                                         ¨ 
                                       
                                       + 
                                       
                                         θ 
                                         ¨ 
                                       
                                     
                                     ) 
                                   
                                    
                                   
                                     m 
                                     
                                       aw 
                                        
                                       
                                           
                                       
                                        
                                       1 
                                        
                                       n 
                                     
                                   
                                    
                                   
                                     cos 
                                      
                                     
                                       ( 
                                       
                                         α 
                                         + 
                                         
                                           γ 
                                           n 
                                         
                                         + 
                                         
                                           θ 
                                           n 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                 - 
                                 
                                   
                                     
                                       ( 
                                       
                                         
                                           α 
                                           . 
                                         
                                         + 
                                         
                                           
                                             θ 
                                             . 
                                           
                                           n 
                                         
                                       
                                       ) 
                                     
                                     2 
                                   
                                    
                                   
                                     m 
                                     
                                       aw 
                                        
                                       
                                           
                                       
                                        
                                       1 
                                        
                                       n 
                                     
                                   
                                    
                                   
                                     sin 
                                      
                                     
                                       ( 
                                       
                                         α 
                                         + 
                                         
                                           γ 
                                           n 
                                         
                                         + 
                                         
                                           θ 
                                           n 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                 - 
                                 
                                    
                                   
                                     
                                        
                                       
                                         
                                           ( 
                                           
                                             
                                               α 
                                               ¨ 
                                             
                                             + 
                                             
                                               
                                                 θ 
                                                 ¨ 
                                               
                                               n 
                                             
                                           
                                           ) 
                                         
                                          
                                         
                                           z 
                                           
                                             6 
                                              
                                             n 
                                           
                                         
                                          
                                         
                                           m 
                                           sn 
                                         
                                       
                                        
                                     
                                      
                                     
                                        
                                       
                                         
                                           sin 
                                            
                                           
                                             ( 
                                             
                                               α 
                                               + 
                                               
                                                 γ 
                                                 n 
                                               
                                               + 
                                               
                                                 η 
                                                 n 
                                               
                                             
                                             ) 
                                           
                                         
                                         - 
                                         
                                           
                                             
                                               ( 
                                               
                                                 
                                                   α 
                                                   . 
                                                 
                                                 + 
                                                 
                                                   
                                                     θ 
                                                     . 
                                                   
                                                   n 
                                                 
                                               
                                               ) 
                                             
                                             2 
                                           
                                            
                                           
                                             z 
                                             
                                               6 
                                                
                                               n 
                                             
                                           
                                            
                                           
                                             m 
                                             sn 
                                           
                                            
                                           
                                             cos 
                                              
                                             
                                               ( 
                                               
                                                 α 
                                                 + 
                                                 
                                                   γ 
                                                   n 
                                                 
                                                 + 
                                                 
                                                   η 
                                                   n 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                         - 
                                         
                                           
                                             α 
                                             ¨ 
                                           
                                            
                                           
                                             m 
                                             sawcn 
                                           
                                            
                                           
                                             sin 
                                              
                                             
                                               ( 
                                               
                                                 α 
                                                 + 
                                                 
                                                   γ 
                                                   n 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                         - 
                                         
                                           
                                             
                                               α 
                                               . 
                                             
                                             2 
                                           
                                            
                                           
                                             m 
                                             sawcn 
                                           
                                            
                                           
                                             cos 
                                              
                                             
                                               ( 
                                               
                                                 α 
                                                 + 
                                                 
                                                   γ 
                                                   n 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                         + 
                                         
                                           
                                             α 
                                             ¨ 
                                           
                                            
                                           
                                             m 
                                             sawbn 
                                           
                                            
                                           cos 
                                            
                                           
                                               
                                           
                                            
                                           α 
                                         
                                         - 
                                         
                                           
                                             
                                               α 
                                               . 
                                             
                                             2 
                                           
                                            
                                           
                                             m 
                                             sawbn 
                                           
                                            
                                           sin 
                                            
                                           
                                               
                                           
                                            
                                           α 
                                         
                                         - 
                                         
                                           
                                             β 
                                             ¨ 
                                           
                                            
                                           
                                             m 
                                             sawan 
                                           
                                         
                                       
                                     
                                   
                                 
                               
                             
                             } 
                           
                            
                           cos 
                            
                           
                               
                           
                            
                           β 
                         
                         - 
                         
                           2 
                            
                           
                             β 
                             . 
                           
                            
                           
                             { 
                             
                               
                                 
                                   
                                     z 
                                     . 
                                   
                                   
                                     6 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   m 
                                   sn 
                                 
                                  
                                 
                                   cos 
                                    
                                   
                                     ( 
                                     
                                       α 
                                       + 
                                       
                                         γ 
                                         n 
                                       
                                       + 
                                       
                                         η 
                                         n 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               + 
                               
                                 
                                   ( 
                                   
                                     
                                       α 
                                       . 
                                     
                                     + 
                                     
                                       
                                         θ 
                                         . 
                                       
                                       n 
                                     
                                   
                                   ) 
                                 
                                  
                                 
                                   m 
                                   
                                     aw 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   cos 
                                    
                                   
                                     ( 
                                     
                                       α 
                                       + 
                                       
                                         γ 
                                         n 
                                       
                                       + 
                                       
                                         θ 
                                         n 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               - 
                               
                                 
                                   ( 
                                   
                                     
                                       α 
                                       . 
                                     
                                     + 
                                     
                                       
                                         η 
                                         . 
                                       
                                       n 
                                     
                                   
                                   ) 
                                 
                                  
                                 
                                   z 
                                   
                                     6 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   m 
                                   sn 
                                 
                                  
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       α 
                                       + 
                                       
                                         γ 
                                         n 
                                       
                                       + 
                                       
                                         η 
                                         n 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               - 
                               
                                 
                                   α 
                                   . 
                                 
                                  
                                 
                                   m 
                                   sawcn 
                                 
                                  
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       α 
                                       + 
                                       
                                         γ 
                                         n 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               + 
                               
                                 
                                   α 
                                   . 
                                 
                                  
                                 
                                   m 
                                   sawbn 
                                 
                                  
                                 cos 
                                  
                                 
                                     
                                 
                                  
                                 α 
                               
                             
                             } 
                           
                            
                           sin 
                            
                           
                               
                           
                            
                           β 
                         
                         - 
                         
                           
                             ( 
                             
                               
                                 
                                   β 
                                   ¨ 
                                 
                                  
                                 sin 
                                  
                                 
                                     
                                 
                                  
                                 β 
                               
                               + 
                               
                                 
                                   
                                     β 
                                     . 
                                   
                                   2 
                                 
                                  
                                 cos 
                                  
                                 
                                     
                                 
                                  
                                 β 
                               
                             
                             ) 
                           
                            
                           
                             { 
                             
                               
                                 
                                   m 
                                   
                                     aw 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       α 
                                       + 
                                       
                                         γ 
                                         n 
                                       
                                       + 
                                       
                                         θ 
                                         n 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               + 
                               
                                 
                                   z 
                                   
                                     6 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   m 
                                   sn 
                                 
                                  
                                 
                                   cos 
                                    
                                   
                                     ( 
                                     
                                       α 
                                       + 
                                       
                                         γ 
                                         n 
                                       
                                       + 
                                       
                                         η 
                                         n 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               + 
                               
                                 
                                   m 
                                   sawcn 
                                 
                                  
                                 
                                   cos 
                                    
                                   
                                     ( 
                                     
                                       α 
                                       + 
                                       
                                         γ 
                                         n 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               + 
                               
                                 
                                   m 
                                   sawbn 
                                 
                                  
                                 sin 
                                  
                                 
                                     
                                 
                                  
                                 α 
                               
                             
                             } 
                           
                         
                         + 
                         
                           g 
                            
                           
                             ( 
                             
                               
                                 m 
                                 b 
                               
                               + 
                               
                                 m 
                                 sawn 
                               
                             
                             ) 
                           
                         
                       
                       = 
                       
                         λ 
                         
                           3 
                            
                           n 
                         
                       
                     
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       z 
                       ¨ 
                     
                     0 
                   
                   = 
                   
                     
                       λ 
                       
                         3 
                          
                         n 
                       
                     
                     - 
                     g 
                     - 
                     
                       
                         
                           
                             α 
                             ¨ 
                           
                            
                           
                             m 
                             b 
                           
                            
                           
                             C 
                             β 
                           
                            
                           
                             A 
                             2 
                           
                         
                         - 
                         
                           
                             
                               α 
                               . 
                             
                             2 
                           
                            
                           
                             m 
                             b 
                           
                            
                           
                             A 
                             1 
                           
                         
                         - 
                         
                           
                             β 
                             ¨ 
                           
                            
                           
                             { 
                             
                               
                                 
                                   m 
                                   ba 
                                 
                                  
                                 
                                   C 
                                   β 
                                 
                               
                               + 
                               
                                 
                                   m 
                                   b 
                                 
                                  
                                 
                                   A 
                                   1 
                                 
                                  
                                 
                                   S 
                                   β 
                                 
                               
                             
                             } 
                           
                         
                         + 
                         
                           
                             β 
                             . 
                           
                            
                           
                             { 
                             
                               
                                 
                                   m 
                                   ba 
                                 
                                  
                                 
                                   S 
                                   β 
                                 
                               
                               + 
                               
                                 
                                   β 
                                   . 
                                 
                                  
                                 
                                   m 
                                   b 
                                 
                                  
                                 
                                   A 
                                   1 
                                 
                                  
                                 
                                   C 
                                   β 
                                 
                               
                             
                             } 
                           
                         
                         + 
                         
                           
 
                         
                          
                         
                             
                         
                          
                         
                           
                             { 
                             
                               
                                 
                                   
                                     z 
                                     ¨ 
                                   
                                   
                                     6 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   m 
                                   sn 
                                 
                                  
                                 
                                   C 
                                   αγη 
                                 
                               
                               - 
                               
                                 2 
                                  
                                 
                                   ( 
                                   
                                     
                                       α 
                                       . 
                                     
                                     + 
                                     
                                       
                                         η 
                                         . 
                                       
                                       n 
                                     
                                   
                                   ) 
                                 
                                  
                                 
                                   
                                     z 
                                     . 
                                   
                                   
                                     6 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   m 
                                   sn 
                                 
                                  
                                 
                                   S 
                                   αγη 
                                 
                               
                               + 
                               
                                 
                                   ( 
                                   
                                     
                                       α 
                                       ¨ 
                                     
                                     + 
                                     
                                       
                                         θ 
                                         ¨ 
                                       
                                       n 
                                     
                                   
                                   ) 
                                 
                                  
                                 
                                   m 
                                   
                                     aw 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   C 
                                   αγη 
                                 
                               
                               - 
                               
                                 
 
                               
                                
                               
                                   
                               
                                
                               
                                 
                                   
                                     ( 
                                     
                                       
                                         α 
                                         . 
                                       
                                       + 
                                       
                                         
                                           θ 
                                           . 
                                         
                                         n 
                                       
                                     
                                     ) 
                                   
                                   2 
                                 
                                  
                                 
                                   m 
                                   
                                     aw 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   S 
                                   αγη 
                                 
                               
                               - 
                               
                                 
                                   ( 
                                   
                                     
                                       α 
                                       ¨ 
                                     
                                     + 
                                     
                                       
                                         η 
                                         ¨ 
                                       
                                       n 
                                     
                                   
                                   ) 
                                 
                                  
                                 
                                   z 
                                   
                                     6 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   m 
                                   sn 
                                 
                                  
                                 
                                   S 
                                   αγη 
                                 
                               
                               - 
                               
                                 
                                   
                                     ( 
                                     
                                       
                                         α 
                                         . 
                                       
                                       + 
                                       
                                         
                                           η 
                                           . 
                                         
                                         n 
                                       
                                     
                                     ) 
                                   
                                   2 
                                 
                                  
                                 
                                   z 
                                   
                                     6 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   m 
                                   sn 
                                 
                                  
                                 
                                   C 
                                   αγη 
                                 
                               
                               - 
                               
                                 
 
                               
                                
                               
                                 
                                   α 
                                   ¨ 
                                 
                                  
                                 
                                   m 
                                   sawcn 
                                 
                                  
                                 
                                   S 
                                   αγη 
                                 
                               
                               - 
                               
                                 
                                   
                                     α 
                                     . 
                                   
                                   2 
                                 
                                  
                                 
                                   m 
                                   sawcn 
                                 
                                  
                                 
                                   C 
                                   αγη 
                                 
                               
                               + 
                               
                                 
                                   α 
                                   ¨ 
                                 
                                  
                                 
                                   m 
                                   sawcn 
                                 
                                  
                                 
                                   C 
                                   α 
                                 
                               
                               - 
                               
                                 
                                   
                                     α 
                                     . 
                                   
                                   2 
                                 
                                  
                                 
                                   m 
                                   sawbn 
                                 
                                  
                                 
                                   S 
                                   α 
                                 
                               
                               - 
                               
                                 
                                   β 
                                   ¨ 
                                 
                                  
                                 
                                   m 
                                   sawan 
                                 
                               
                             
                             } 
                           
                            
                           
                             C 
                             β 
                           
                         
                         - 
                         
                           
 
                         
                          
                         
                             
                         
                          
                         
                           2 
                            
                           
                             β 
                             . 
                           
                            
                           
                             { 
                             
                               
                                 
                                   
                                     z 
                                     . 
                                   
                                   
                                     6 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   m 
                                   sn 
                                 
                                  
                                 
                                   C 
                                   αγη 
                                 
                               
                               + 
                               
                                 
                                   ( 
                                   
                                     
                                       α 
                                       . 
                                     
                                     + 
                                     
                                       
                                         θ 
                                         . 
                                       
                                       n 
                                     
                                   
                                   ) 
                                 
                                  
                                 
                                   m 
                                   
                                     aw 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   C 
                                   αγη 
                                 
                               
                               - 
                               
                                 
                                   ( 
                                   
                                     
                                       α 
                                       . 
                                     
                                     + 
                                     
                                       
                                         η 
                                         . 
                                       
                                       n 
                                     
                                   
                                   ) 
                                 
                                  
                                 
                                   z 
                                   
                                     6 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   m 
                                   sn 
                                 
                                  
                                 
                                   S 
                                   αγη 
                                 
                               
                               - 
                               
                                 
 
                               
                                
                               
                                   
                               
                                
                               
                                 
                                   α 
                                   . 
                                 
                                  
                                 
                                   m 
                                   sawcn 
                                 
                                  
                                 
                                   S 
                                   αγη 
                                 
                               
                               + 
                               
                                 
                                   α 
                                   . 
                                 
                                  
                                 
                                   m 
                                   sawbn 
                                 
                                  
                                 
                                   C 
                                   α 
                                 
                               
                               - 
                               
                                 
                                   β 
                                   . 
                                 
                                  
                                 
                                   
                                     m 
                                     sawan 
                                   
                                   / 
                                   2 
                                 
                               
                             
                             } 
                           
                            
                           S 
                            
                           
                               
                           
                            
                           β 
                         
                         - 
                         
                           
 
                         
                          
                         
                             
                         
                          
                         
                           
                             ( 
                             
                               
                                 
                                   β 
                                   ¨ 
                                 
                                  
                                 
                                   S 
                                   β 
                                 
                               
                               + 
                               
                                 
                                   
                                     β 
                                     . 
                                   
                                   2 
                                 
                                  
                                 
                                   C 
                                   β 
                                 
                               
                             
                             ) 
                           
                            
                           
                             { 
                             
                               
                                 
                                   m 
                                   
                                     aw 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   S 
                                   αγη 
                                 
                               
                               + 
                               
                                 
                                   z 
                                   
                                     6 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   m 
                                   sn 
                                 
                                  
                                 
                                   C 
                                   αγη 
                                 
                               
                               + 
                               
                                 
                                   m 
                                   sawcn 
                                 
                                  
                                 
                                   C 
                                   αγη 
                                 
                               
                               + 
                               
                                 
                                   m 
                                   sawbn 
                                 
                                  
                                 
                                   S 
                                   α 
                                 
                               
                             
                             } 
                           
                         
                       
                       
                         m 
                         bsawn 
                       
                     
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         
                            
                           
                              
                             t 
                           
                         
                          
                         
                           ( 
                           
                             
                               ∂ 
                               L 
                             
                             
                               ∂ 
                               
                                 β 
                                 . 
                               
                             
                           
                           ) 
                         
                       
                       - 
                       
                         
                           ∂ 
                           L 
                         
                         
                           ∂ 
                           β 
                         
                       
                     
                     = 
                     
                       
                         
                           
                             ∂ 
                             F 
                           
                           
                             ∂ 
                             
                               β 
                               . 
                             
                           
                         
                         + 
                         
                           
                             ∑ 
                             
                               l 
                               , 
                               n 
                             
                           
                            
                           
                             
                               λ 
                               
                                 l 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                              
                             
                               a 
                               
                                 l 
                                  
                                 
                                     
                                 
                                  
                                 n 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                              
                             
                                 
                             
                              
                             l 
                           
                         
                       
                       = 
                       1 
                     
                   
                   , 
                   2 
                   , 
                   
                     
                       3 
                        
                       
                           
                       
                        
                       n 
                     
                     = 
                     i 
                   
                   , 
                   ii 
                   , 
                   iii 
                   , 
                   iv 
                 
               
               
                 
                   ( 
                   5.89 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 
                                   
                                     
                                       β 
                                       ¨ 
                                     
                                      
                                     
                                       〈 
                                       
                                         
                                           m 
                                           saw2n 
                                         
                                         + 
                                         
                                           m 
                                           baI 
                                         
                                         + 
                                         
                                           
                                             
                                               m 
                                               b 
                                             
                                              
                                             
                                               ( 
                                               
                                                 
                                                   
                                                     b 
                                                     0 
                                                   
                                                    
                                                   sin 
                                                    
                                                   
                                                       
                                                   
                                                    
                                                   α 
                                                 
                                                 + 
                                                 
                                                   
                                                     c 
                                                     0 
                                                   
                                                    
                                                   cos 
                                                    
                                                   
                                                       
                                                   
                                                    
                                                   α 
                                                 
                                               
                                               ) 
                                             
                                           
                                           2 
                                         
                                         + 
                                         
                                           
                                             m 
                                             sn 
                                           
                                            
                                           
                                             
                                               { 
                                               
                                                 
                                                   
                                                     z 
                                                     
                                                       6 
                                                        
                                                       n 
                                                     
                                                   
                                                    
                                                   
                                                     cos 
                                                      
                                                     
                                                       ( 
                                                       
                                                         α 
                                                         + 
                                                         
                                                           γ 
                                                           n 
                                                         
                                                         + 
                                                         
                                                           η 
                                                           n 
                                                         
                                                       
                                                       ) 
                                                     
                                                   
                                                 
                                                 + 
                                                 
                                                   
                                                     c 
                                                     
                                                       1 
                                                        
                                                       n 
                                                     
                                                   
                                                    
                                                   
                                                     cos 
                                                      
                                                     
                                                       ( 
                                                       
                                                         α 
                                                         + 
                                                         
                                                           γ 
                                                           n 
                                                         
                                                       
                                                       ) 
                                                     
                                                   
                                                 
                                                 + 
                                                 
                                                   
                                                     b 
                                                     
                                                       2 
                                                        
                                                       n 
                                                     
                                                   
                                                    
                                                   sin 
                                                    
                                                   
                                                       
                                                   
                                                    
                                                   α 
                                                 
                                               
                                               } 
                                             
                                             2 
                                           
                                         
                                         + 
                                         
                                           
                                             m 
                                             an 
                                           
                                            
                                           
                                             
                                               { 
                                               
                                                 
                                                   
                                                     e 
                                                     
                                                       1 
                                                        
                                                       n 
                                                     
                                                   
                                                    
                                                   
                                                     sin 
                                                      
                                                     
                                                       ( 
                                                       
                                                         α 
                                                         + 
                                                         
                                                           γ 
                                                           n 
                                                         
                                                         + 
                                                         
                                                           θ 
                                                           n 
                                                         
                                                       
                                                       ) 
                                                     
                                                   
                                                 
                                                 + 
                                                 
                                                   
                                                     c 
                                                     
                                                       2 
                                                        
                                                       n 
                                                     
                                                   
                                                    
                                                   
                                                     cos 
                                                      
                                                     
                                                       ( 
                                                       
                                                         α 
                                                         + 
                                                         
                                                           γ 
                                                           n 
                                                         
                                                       
                                                       ) 
                                                     
                                                   
                                                 
                                                 + 
                                                 
                                                   
                                                     b 
                                                     
                                                       2 
                                                        
                                                       n 
                                                     
                                                   
                                                    
                                                   sin 
                                                    
                                                   
                                                       
                                                   
                                                    
                                                   α 
                                                 
                                               
                                               } 
                                             
                                             2 
                                           
                                         
                                         + 
                                         
                                           
                                             m 
                                             wn 
                                           
                                            
                                           
                                             
                                               { 
                                               
                                                 
                                                   
                                                     e 
                                                     
                                                       3 
                                                        
                                                       n 
                                                     
                                                   
                                                    
                                                   
                                                     sin 
                                                      
                                                     
                                                       ( 
                                                       
                                                         α 
                                                         + 
                                                         
                                                           γ 
                                                           n 
                                                         
                                                         + 
                                                         
                                                           θ 
                                                           n 
                                                         
                                                       
                                                       ) 
                                                     
                                                   
                                                 
                                                 + 
                                                 
                                                   
                                                     c 
                                                     
                                                       2 
                                                        
                                                       n 
                                                     
                                                   
                                                    
                                                   
                                                     cos 
                                                      
                                                     
                                                       ( 
                                                       
                                                         α 
                                                         + 
                                                         
                                                           γ 
                                                           n 
                                                         
                                                       
                                                       ) 
                                                     
                                                   
                                                 
                                                 + 
                                                 
                                                   
                                                     b 
                                                     
                                                       2 
                                                        
                                                       n 
                                                     
                                                   
                                                    
                                                   sin 
                                                    
                                                   
                                                       
                                                   
                                                    
                                                   α 
                                                 
                                               
                                               } 
                                             
                                             2 
                                           
                                         
                                       
                                       〉 
                                     
                                   
                                   + 
                                   
                                     2 
                                      
                                     
                                       β 
                                       . 
                                     
                                      
                                     
                                       〈 
                                       
                                         
                                           
                                             α 
                                             . 
                                           
                                            
                                           
                                             
                                               m 
                                               b 
                                             
                                              
                                             
                                               ( 
                                               
                                                 
                                                   
                                                     b 
                                                     0 
                                                   
                                                    
                                                   sin 
                                                    
                                                   
                                                       
                                                   
                                                    
                                                   α 
                                                 
                                                 + 
                                                 
                                                   
                                                     c 
                                                     0 
                                                   
                                                    
                                                   cos 
                                                    
                                                   
                                                       
                                                   
                                                    
                                                   α 
                                                 
                                               
                                               ) 
                                             
                                           
                                            
                                           
                                             ( 
                                             
                                               
                                                 
                                                   b 
                                                   0 
                                                 
                                                  
                                                 cos 
                                                  
                                                 
                                                     
                                                 
                                                  
                                                 α 
                                               
                                                
                                               
                                                   
                                               
                                               - 
                                               
                                                 
                                                   c 
                                                   0 
                                                 
                                                  
                                                 sin 
                                                  
                                                 
                                                     
                                                 
                                                  
                                                 α 
                                               
                                             
                                             ) 
                                           
                                         
                                         + 
                                         
                                           
                                             m 
                                             sn 
                                           
                                            
                                           
                                             { 
                                             
                                               
                                                 
                                                   z 
                                                   
                                                     6 
                                                      
                                                     n 
                                                   
                                                 
                                                  
                                                 
                                                   cos 
                                                    
                                                   
                                                     ( 
                                                     
                                                       α 
                                                       + 
                                                       
                                                         γ 
                                                         n 
                                                       
                                                       + 
                                                       
                                                         η 
                                                         n 
                                                       
                                                     
                                                     ) 
                                                   
                                                 
                                               
                                               + 
                                               
                                                 
                                                   c 
                                                   
                                                     1 
                                                      
                                                     n 
                                                   
                                                 
                                                  
                                                 
                                                   cos 
                                                    
                                                   
                                                     ( 
                                                     
                                                       α 
                                                       + 
                                                       
                                                         γ 
                                                         n 
                                                       
                                                     
                                                     ) 
                                                   
                                                 
                                               
                                               + 
                                               
                                                 
                                                   b 
                                                   
                                                     2 
                                                      
                                                     n 
                                                   
                                                 
                                                  
                                                 sin 
                                                  
                                                 
                                                     
                                                 
                                                  
                                                 α 
                                               
                                             
                                             } 
                                           
                                            
                                           
                                             { 
                                             
                                               
                                                 
                                                   
                                                     z 
                                                     . 
                                                   
                                                   
                                                     6 
                                                      
                                                     n 
                                                   
                                                 
                                                  
                                                 
                                                   cos 
                                                    
                                                   
                                                     ( 
                                                     
                                                       α 
                                                       + 
                                                       
                                                         γ 
                                                         n 
                                                       
                                                       + 
                                                       
                                                         η 
                                                         n 
                                                       
                                                     
                                                     ) 
                                                   
                                                 
                                               
                                               - 
                                               
                                                 
                                                   ( 
                                                   
                                                     
                                                       α 
                                                       . 
                                                     
                                                     + 
                                                     
                                                       
                                                         η 
                                                         . 
                                                       
                                                       n 
                                                     
                                                   
                                                   ) 
                                                 
                                                  
                                                 
                                                   z 
                                                   
                                                     6 
                                                      
                                                     n 
                                                   
                                                 
                                                  
                                                 
                                                   sin 
                                                    
                                                   
                                                     ( 
                                                     
                                                       α 
                                                       + 
                                                       
                                                         γ 
                                                         n 
                                                       
                                                       + 
                                                       
                                                         η 
                                                         n 
                                                       
                                                     
                                                     ) 
                                                   
                                                 
                                               
                                               - 
                                               
                                                 
                                                   α 
                                                   . 
                                                 
                                                  
                                                 
                                                   [ 
                                                   
                                                     
                                                       
                                                         c 
                                                         
                                                           1 
                                                            
                                                           n 
                                                         
                                                       
                                                        
                                                       
                                                         sin 
                                                          
                                                         
                                                           ( 
                                                           
                                                             α 
                                                             + 
                                                             
                                                             γ 
                                                             n 
                                                             
                                                           
                                                           ) 
                                                         
                                                       
                                                     
                                                     - 
                                                     
                                                       
                                                         b 
                                                         
                                                           2 
                                                            
                                                           n 
                                                         
                                                       
                                                        
                                                       cos 
                                                        
                                                       
                                                           
                                                       
                                                        
                                                       α 
                                                     
                                                   
                                                   ] 
                                                 
                                               
                                             
                                             } 
                                           
                                         
                                         + 
                                         
                                           
                                             m 
                                             an 
                                           
                                            
                                           
                                             { 
                                             
                                               
                                                 
                                                   e 
                                                   
                                                     
                                                       1 
                                                        
                                                       n 
                                                     
                                                      
                                                     
                                                         
                                                     
                                                   
                                                 
                                                  
                                                 
                                                   sin 
                                                    
                                                   
                                                     ( 
                                                     
                                                       α 
                                                       + 
                                                       
                                                         γ 
                                                         n 
                                                       
                                                       + 
                                                       
                                                         θ 
                                                         n 
                                                       
                                                     
                                                     ) 
                                                   
                                                 
                                               
                                               + 
                                               
                                                 
                                                   c 
                                                   
                                                     
                                                       2 
                                                        
                                                       n 
                                                     
                                                      
                                                     
                                                         
                                                     
                                                   
                                                 
                                                  
                                                 
                                                   cos 
                                                    
                                                   
                                                     ( 
                                                     
                                                       α 
                                                       + 
                                                       
                                                         γ 
                                                         n 
                                                       
                                                     
                                                     ) 
                                                   
                                                 
                                               
                                               + 
                                               
                                                 
                                                   b 
                                                   
                                                     
                                                       2 
                                                        
                                                       n 
                                                     
                                                      
                                                     
                                                         
                                                     
                                                   
                                                 
                                                  
                                                 sin 
                                                  
                                                 
                                                     
                                                 
                                                  
                                                 α 
                                               
                                             
                                             } 
                                           
                                            
                                           
                                             { 
                                             
                                               
                                                 
                                                   ( 
                                                   
                                                     
                                                       α 
                                                       . 
                                                     
                                                     + 
                                                     
                                                       
                                                         θ 
                                                         . 
                                                       
                                                       n 
                                                     
                                                   
                                                   ) 
                                                 
                                                  
                                                 
                                                   e 
                                                   
                                                     1 
                                                      
                                                     n 
                                                   
                                                 
                                                  
                                                 
                                                   cos 
                                                    
                                                   
                                                     ( 
                                                     
                                                       α 
                                                       + 
                                                       
                                                         γ 
                                                         n 
                                                       
                                                       + 
                                                       
                                                         θ 
                                                         n 
                                                       
                                                     
                                                     ) 
                                                   
                                                 
                                               
                                               - 
                                               
                                                 
                                                   α 
                                                   . 
                                                 
                                                  
                                                 
                                                   [ 
                                                   
                                                     
                                                       
                                                         c 
                                                         
                                                           2 
                                                            
                                                           n 
                                                         
                                                       
                                                        
                                                       
                                                         sin 
                                                          
                                                         
                                                           ( 
                                                           
                                                             α 
                                                             + 
                                                             
                                                             γ 
                                                             n 
                                                             
                                                           
                                                           ) 
                                                         
                                                       
                                                     
                                                     - 
                                                     
                                                       
                                                         b 
                                                         
                                                           2 
                                                            
                                                           n 
                                                         
                                                       
                                                        
                                                       cos 
                                                        
                                                       
                                                           
                                                       
                                                        
                                                       α 
                                                     
                                                   
                                                   ] 
                                                 
                                               
                                             
                                             } 
                                           
                                         
                                         + 
                                         
                                           
                                             m 
                                             wn 
                                           
                                            
                                           
                                             { 
                                             
                                               
                                                 
                                                   e 
                                                   
                                                     3 
                                                      
                                                     n 
                                                   
                                                 
                                                  
                                                 
                                                   sin 
                                                    
                                                   
                                                     ( 
                                                     
                                                       α 
                                                       + 
                                                       
                                                         γ 
                                                         n 
                                                       
                                                       + 
                                                       
                                                         θ 
                                                         n 
                                                       
                                                     
                                                     ) 
                                                   
                                                 
                                               
                                               + 
                                               
                                                 
                                                   c 
                                                   
                                                     2 
                                                      
                                                     n 
                                                   
                                                 
                                                  
                                                 
                                                   cos 
                                                    
                                                   
                                                     ( 
                                                     
                                                       α 
                                                       + 
                                                       
                                                         γ 
                                                         n 
                                                       
                                                     
                                                     ) 
                                                   
                                                 
                                               
                                               + 
                                               
                                                 
                                                   b 
                                                   
                                                     2 
                                                      
                                                     n 
                                                   
                                                 
                                                  
                                                 sin 
                                                  
                                                 
                                                     
                                                 
                                                  
                                                 α 
                                               
                                             
                                             } 
                                           
                                            
                                           
                                             { 
                                             
                                               
                                                 
                                                   ( 
                                                   
                                                     
                                                       α 
                                                       . 
                                                     
                                                     + 
                                                     
                                                       
                                                         θ 
                                                         . 
                                                       
                                                       n 
                                                     
                                                   
                                                   ) 
                                                 
                                                  
                                                 
                                                   e 
                                                   
                                                     3 
                                                      
                                                     n 
                                                   
                                                 
                                                  
                                                 
                                                   sin 
                                                    
                                                   
                                                     ( 
                                                     
                                                       α 
                                                       + 
                                                       
                                                         γ 
                                                         n 
                                                       
                                                       + 
                                                       
                                                         θ 
                                                         n 
                                                       
                                                     
                                                     ) 
                                                   
                                                 
                                               
                                               - 
                                               
                                                 
                                                   α 
                                                   . 
                                                 
                                                  
                                                 
                                                   [ 
                                                   
                                                     
                                                       
                                                         c 
                                                         
                                                           2 
                                                            
                                                           n 
                                                         
                                                       
                                                        
                                                       
                                                         sin 
                                                          
                                                         
                                                           ( 
                                                           
                                                             α 
                                                             + 
                                                             
                                                             γ 
                                                             n 
                                                             
                                                           
                                                           ) 
                                                         
                                                       
                                                     
                                                     - 
                                                     
                                                       
                                                         b 
                                                         
                                                           2 
                                                            
                                                           n 
                                                         
                                                       
                                                        
                                                       cos 
                                                        
                                                       
                                                           
                                                       
                                                        
                                                       α 
                                                     
                                                   
                                                   ] 
                                                 
                                               
                                             
                                             } 
                                           
                                         
                                       
                                       〉 
                                     
                                   
                                   - 
                                   
                                     
                                       α 
                                       ¨ 
                                     
                                      
                                     
                                       
                                         m 
                                         ba 
                                       
                                        
                                       
                                         ( 
                                         
                                           
                                             
                                               b 
                                               0 
                                             
                                              
                                             cos 
                                              
                                             
                                                 
                                             
                                              
                                             α 
                                           
                                           - 
                                           
                                             
                                               c 
                                               0 
                                             
                                              
                                             sin 
                                              
                                             
                                                 
                                             
                                              
                                             α 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                   + 
                                   
                                     
                                       
                                         α 
                                         . 
                                       
                                       2 
                                     
                                      
                                     
                                       
                                         m 
                                         ba 
                                       
                                        
                                       
                                         ( 
                                         
                                           
                                             
                                               b 
                                               0 
                                             
                                              
                                             sin 
                                              
                                             
                                                 
                                             
                                              
                                             α 
                                           
                                           + 
                                           
                                             
                                               c 
                                               0 
                                             
                                              
                                             cos 
                                              
                                             
                                                 
                                             
                                              
                                             α 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                   - 
                                   
                                     
                                       
                                         z 
                                         ¨ 
                                       
                                       
                                         6 
                                          
                                         n 
                                       
                                     
                                      
                                     
                                       m 
                                       sn 
                                     
                                      
                                     
                                       a 
                                       
                                         1 
                                          
                                         n 
                                       
                                     
                                      
                                     
                                       cos 
                                        
                                       
                                         ( 
                                         
                                           α 
                                           + 
                                           
                                             γ 
                                             n 
                                           
                                           + 
                                           
                                             η 
                                             n 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                   + 
                                   
                                     
                                       
                                         
                                           z 
                                           . 
                                         
                                         
                                           6 
                                            
                                           n 
                                         
                                       
                                        
                                       
                                         ( 
                                         
                                           
                                             α 
                                             . 
                                           
                                           + 
                                           
                                             
                                               η 
                                               . 
                                             
                                             n 
                                           
                                         
                                         ) 
                                       
                                     
                                      
                                     
                                       m 
                                       sn 
                                     
                                      
                                     
                                       a 
                                       
                                         1 
                                          
                                         n 
                                       
                                     
                                      
                                     
                                       sin 
                                        
                                       
                                         ( 
                                         
                                           α 
                                           + 
                                           
                                             γ 
                                             n 
                                           
                                           + 
                                           
                                             η 
                                             n 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                   + 
                                   
                                     
                                       
                                         η 
                                         ¨ 
                                       
                                       n 
                                     
                                      
                                     
                                       m 
                                       sn 
                                     
                                      
                                     
                                       z 
                                       
                                         6 
                                          
                                         n 
                                       
                                     
                                      
                                     
                                       a 
                                       
                                         1 
                                          
                                         n 
                                       
                                     
                                      
                                     
                                       sin 
                                        
                                       
                                         ( 
                                         
                                           α 
                                           + 
                                           
                                             γ 
                                             n 
                                           
                                           + 
                                           
                                             η 
                                             n 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                   + 
                                   
                                     
                                       
                                         η 
                                         . 
                                       
                                       n 
                                     
                                      
                                     
                                       m 
                                       sn 
                                     
                                      
                                     
                                       
                                         z 
                                         . 
                                       
                                       
                                         6 
                                          
                                         n 
                                       
                                     
                                      
                                     
                                       a 
                                       
                                         1 
                                          
                                         n 
                                       
                                     
                                      
                                     
                                       sin 
                                        
                                       
                                         ( 
                                         
                                           α 
                                           + 
                                           
                                             γ 
                                             n 
                                           
                                           + 
                                           
                                             η 
                                             n 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                   + 
                                   
                                     
                                       
                                         
                                           η 
                                           . 
                                         
                                         n 
                                       
                                        
                                       
                                         ( 
                                         
                                           
                                             α 
                                             . 
                                           
                                           + 
                                           
                                             
                                               η 
                                               . 
                                             
                                             n 
                                           
                                         
                                         ) 
                                       
                                     
                                      
                                     
                                       m 
                                       sn 
                                     
                                      
                                     
                                       z 
                                       
                                         6 
                                          
                                         n 
                                       
                                     
                                      
                                     
                                       a 
                                       
                                         1 
                                          
                                         n 
                                       
                                     
                                      
                                     
                                       cos 
                                        
                                       
                                         ( 
                                         
                                           α 
                                           + 
                                           
                                             γ 
                                             n 
                                           
                                           + 
                                           
                                             η 
                                             n 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                   - 
                                   
                                     
                                       
                                         θ 
                                         ¨ 
                                       
                                       n 
                                     
                                      
                                     
                                       m 
                                       aw1n 
                                     
                                      
                                     
                                       a 
                                       
                                         1 
                                          
                                         n 
                                       
                                     
                                      
                                     
                                       cos 
                                        
                                       
                                         ( 
                                         
                                           α 
                                           + 
                                           
                                             γ 
                                             n 
                                           
                                           + 
                                           
                                             θ 
                                             n 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                   + 
                                   
                                     
                                       
                                         
                                           θ 
                                           . 
                                         
                                         n 
                                       
                                        
                                       
                                         ( 
                                         
                                           
                                             α 
                                             . 
                                           
                                           + 
                                           
                                             
                                               θ 
                                               . 
                                             
                                             n 
                                           
                                         
                                         ) 
                                       
                                     
                                      
                                     
                                       m 
                                       aw1n 
                                     
                                      
                                     
                                       a 
                                       
                                         1 
                                          
                                         n 
                                       
                                     
                                      
                                     
                                       sin 
                                        
                                       
                                         ( 
                                         
                                           α 
                                           + 
                                           
                                             γ 
                                             n 
                                           
                                           + 
                                           
                                             θ 
                                             n 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                   + 
                                   
                                      
                                     
                                       
                                         
                                           α 
                                           ¨ 
                                         
                                          
                                         
                                           a 
                                           
                                             1 
                                              
                                             n 
                                           
                                         
                                          
                                         
                                           { 
                                           
                                             
                                               
                                                 m 
                                                 sawcn 
                                               
                                                
                                               
                                                 sin 
                                                  
                                                 
                                                   ( 
                                                   
                                                     α 
                                                     + 
                                                     
                                                       γ 
                                                       n 
                                                     
                                                   
                                                   ) 
                                                 
                                               
                                             
                                             - 
                                             
                                               
                                                 m 
                                                 sawbn 
                                               
                                                
                                               cos 
                                                
                                               
                                                   
                                               
                                                
                                               α 
                                             
                                             + 
                                             
                                               
                                                 m 
                                                 sn 
                                               
                                                
                                               
                                                 z 
                                                 
                                                   6 
                                                    
                                                   n 
                                                 
                                               
                                                
                                               
                                                 sin 
                                                  
                                                 
                                                   ( 
                                                   
                                                     α 
                                                     + 
                                                     
                                                       γ 
                                                       n 
                                                     
                                                     + 
                                                     
                                                       η 
                                                       n 
                                                     
                                                   
                                                   ) 
                                                 
                                               
                                             
                                             - 
                                             
                                               
                                                 m 
                                                 aw1n 
                                               
                                                
                                               
                                                 cos 
                                                  
                                                 
                                                   ( 
                                                   
                                                     α 
                                                     + 
                                                     
                                                       γ 
                                                       n 
                                                     
                                                     + 
                                                     
                                                       θ 
                                                       n 
                                                     
                                                   
                                                   ) 
                                                 
                                               
                                             
                                           
                                           } 
                                         
                                       
                                       + 
                                       
                                         
                                           α 
                                           . 
                                         
                                          
                                         
                                           a 
                                           
                                             1 
                                              
                                             n 
                                           
                                         
                                          
                                         
                                           { 
                                           
                                             
                                               
                                                 α 
                                                 . 
                                               
                                                
                                               
                                                 m 
                                                 sawcn 
                                               
                                                
                                               
                                                 cos 
                                                  
                                                 
                                                   ( 
                                                   
                                                     α 
                                                     + 
                                                     
                                                       γ 
                                                       n 
                                                     
                                                   
                                                   ) 
                                                 
                                               
                                             
                                             + 
                                             
                                               
                                                 α 
                                                 . 
                                               
                                                
                                               
                                                 m 
                                                 sawbn 
                                               
                                                
                                               sin 
                                                
                                               
                                                   
                                               
                                                
                                               α 
                                             
                                             + 
                                             
                                               
                                                 ( 
                                                 
                                                   
                                                     α 
                                                     . 
                                                   
                                                   + 
                                                   
                                                     
                                                       η 
                                                       . 
                                                     
                                                     n 
                                                   
                                                 
                                                 ) 
                                               
                                                
                                               
                                                 m 
                                                 sn 
                                               
                                                
                                               
                                                 z 
                                                 
                                                   6 
                                                    
                                                   n 
                                                 
                                               
                                                
                                               
                                                 cos 
                                                  
                                                 
                                                   ( 
                                                   
                                                     α 
                                                     + 
                                                     
                                                       γ 
                                                       n 
                                                     
                                                     + 
                                                     
                                                       η 
                                                       n 
                                                     
                                                   
                                                   ) 
                                                 
                                               
                                             
                                             + 
                                             
                                               
                                                 m 
                                                 sn 
                                               
                                                
                                               
                                                 
                                                   z 
                                                   . 
                                                 
                                                 
                                                   6 
                                                    
                                                   n 
                                                 
                                               
                                                
                                               
                                                 sin 
                                                  
                                                 
                                                   ( 
                                                   
                                                     α 
                                                     + 
                                                     
                                                       γ 
                                                       n 
                                                     
                                                     + 
                                                     
                                                       η 
                                                       n 
                                                     
                                                   
                                                   ) 
                                                 
                                               
                                             
                                             + 
                                             
                                               
                                                 ( 
                                                 
                                                   
                                                     α 
                                                     . 
                                                   
                                                   + 
                                                   
                                                     
                                                       θ 
                                                       . 
                                                     
                                                     n 
                                                   
                                                 
                                                 ) 
                                               
                                                
                                               
                                                 m 
                                                 aw1n 
                                               
                                                
                                               
                                                 sin 
                                                  
                                                 
                                                   ( 
                                                   
                                                     α 
                                                     + 
                                                     
                                                       γ 
                                                       n 
                                                     
                                                     + 
                                                     
                                                       θ 
                                                       n 
                                                     
                                                   
                                                   ) 
                                                 
                                               
                                             
                                           
                                           } 
                                         
                                       
                                       - 
                                       
                                         
                                           
                                             z 
                                             ¨ 
                                           
                                           0 
                                         
                                          
                                         
                                           [ 
                                           
                                             
                                               
                                                 { 
                                                 
                                                   
                                                     
                                                       m 
                                                       b 
                                                     
                                                      
                                                     
                                                       ( 
                                                       
                                                         
                                                           
                                                             b 
                                                             0 
                                                           
                                                            
                                                           sin 
                                                            
                                                           
                                                               
                                                           
                                                            
                                                           α 
                                                         
                                                         + 
                                                         
                                                           
                                                             c 
                                                             0 
                                                           
                                                            
                                                           cos 
                                                            
                                                           
                                                               
                                                           
                                                            
                                                           α 
                                                         
                                                       
                                                       ) 
                                                     
                                                   
                                                   + 
                                                   
                                                     
                                                       m 
                                                       aw1n 
                                                     
                                                      
                                                     
                                                       sin 
                                                        
                                                       
                                                         ( 
                                                         
                                                           α 
                                                           + 
                                                           
                                                             γ 
                                                             n 
                                                           
                                                           + 
                                                           
                                                             θ 
                                                             n 
                                                           
                                                         
                                                         ) 
                                                       
                                                     
                                                   
                                                   + 
                                                   
                                                     
                                                       z 
                                                       
                                                         6 
                                                          
                                                         n 
                                                       
                                                     
                                                      
                                                     
                                                       m 
                                                       sn 
                                                     
                                                      
                                                     
                                                       cos 
                                                        
                                                       
                                                         ( 
                                                         
                                                           α 
                                                           + 
                                                           
                                                             γ 
                                                             n 
                                                           
                                                           + 
                                                           
                                                             η 
                                                             n 
                                                           
                                                         
                                                         ) 
                                                       
                                                     
                                                   
                                                   + 
                                                   
                                                     
                                                       m 
                                                       sawcn 
                                                     
                                                      
                                                     
                                                       cos 
                                                        
                                                       
                                                         ( 
                                                         
                                                           α 
                                                           + 
                                                           γ 
                                                         
                                                         ) 
                                                       
                                                     
                                                   
                                                   + 
                                                   
                                                     
                                                       m 
                                                       sawbn 
                                                     
                                                      
                                                     sin 
                                                      
                                                     
                                                         
                                                     
                                                      
                                                     α 
                                                   
                                                 
                                                 } 
                                               
                                                
                                               sin 
                                                
                                               
                                                   
                                               
                                                
                                               β 
                                             
                                             + 
                                             
                                               ( 
                                               
                                                 
                                                   m 
                                                   ba 
                                                 
                                                 + 
                                                 
                                                   
                                                     m 
                                                     sawan 
                                                   
                                                    
                                                   cos 
                                                    
                                                   
                                                       
                                                   
                                                    
                                                   β 
                                                 
                                               
                                               ) 
                                             
                                           
                                           ] 
                                         
                                       
                                       - 
                                       
                                         
                                           
                                             z 
                                             . 
                                           
                                           0 
                                         
                                         [ 
                                         
                                           
                                             
                                               { 
                                               
                                                 
                                                   
                                                     α 
                                                     . 
                                                   
                                                    
                                                   
                                                     
                                                       m 
                                                       b 
                                                     
                                                      
                                                     
                                                       ( 
                                                       
                                                         
                                                           
                                                             b 
                                                             0 
                                                           
                                                            
                                                           cos 
                                                            
                                                           
                                                               
                                                           
                                                            
                                                           α 
                                                         
                                                         - 
                                                         
                                                           
                                                             c 
                                                             0 
                                                           
                                                            
                                                           sin 
                                                            
                                                           
                                                               
                                                           
                                                            
                                                           α 
                                                         
                                                       
                                                       ) 
                                                     
                                                   
                                                 
                                                 + 
                                                 
                                                   
                                                     ( 
                                                     
                                                       
                                                         α 
                                                         . 
                                                       
                                                       + 
                                                       
                                                         
                                                           θ 
                                                           . 
                                                         
                                                         n 
                                                       
                                                     
                                                     ) 
                                                   
                                                    
                                                   
                                                     m 
                                                     aw1n 
                                                   
                                                    
                                                   
                                                     cos 
                                                      
                                                     
                                                       ( 
                                                       
                                                         α 
                                                         + 
                                                         
                                                           γ 
                                                           n 
                                                         
                                                         + 
                                                         
                                                           θ 
                                                           n 
                                                         
                                                       
                                                       ) 
                                                     
                                                   
                                                 
                                                 + 
                                                 
                                                   
                                                     
                                                       z 
                                                       . 
                                                     
                                                     
                                                       6 
                                                        
                                                       n 
                                                     
                                                   
                                                    
                                                   
                                                     m 
                                                     sn 
                                                   
                                                    
                                                   
                                                     cos 
                                                      
                                                     
                                                       ( 
                                                       
                                                         α 
                                                         + 
                                                         
                                                           γ 
                                                           n 
                                                         
                                                         + 
                                                         
                                                           η 
                                                           n 
                                                         
                                                       
                                                       ) 
                                                     
                                                   
                                                 
                                                 - 
                                                 
                                                   
                                                     ( 
                                                     
                                                       
                                                         α 
                                                         . 
                                                       
                                                       + 
                                                       
                                                         
                                                           η 
                                                           . 
                                                         
                                                         n 
                                                       
                                                     
                                                     ) 
                                                   
                                                    
                                                   
                                                     z 
                                                     
                                                       6 
                                                        
                                                       n 
                                                     
                                                   
                                                    
                                                   
                                                     m 
                                                     sn 
                                                   
                                                    
                                                   
                                                     sin 
                                                      
                                                     
                                                       ( 
                                                       
                                                         α 
                                                         + 
                                                         
                                                           γ 
                                                           n 
                                                         
                                                         + 
                                                         
                                                           η 
                                                           n 
                                                         
                                                       
                                                       ) 
                                                     
                                                   
                                                 
                                                 - 
                                                 
                                                   
                                                     α 
                                                     . 
                                                   
                                                    
                                                   
                                                     m 
                                                     sawcn 
                                                   
                                                    
                                                   
                                                     sin 
                                                      
                                                     
                                                       ( 
                                                       
                                                         α 
                                                         + 
                                                         
                                                           γ 
                                                           n 
                                                         
                                                       
                                                       ) 
                                                     
                                                   
                                                 
                                                 + 
                                                 
                                                   
                                                     α 
                                                     . 
                                                   
                                                    
                                                   
                                                     m 
                                                     sawbn 
                                                   
                                                    
                                                   cos 
                                                    
                                                   
                                                       
                                                   
                                                    
                                                   α 
                                                 
                                               
                                               } 
                                             
                                              
                                             sin 
                                              
                                             
                                                 
                                             
                                              
                                             β 
                                           
                                           + 
                                           
                                              
                                             
                                               
                                                 β 
                                                 . 
                                               
                                                
                                               
                                                 
                                                   z 
                                                   . 
                                                 
                                                 0 
                                               
                                                
                                               
                                                  
                                                 
                                                   
                                                     
                                                       { 
                                                       
                                                         
                                                           
                                                             m 
                                                             b 
                                                           
                                                            
                                                           
                                                             ( 
                                                             
                                                             
                                                             
                                                             b 
                                                             0 
                                                             
                                                              
                                                             sin 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             α 
                                                             
                                                             + 
                                                             
                                                             
                                                             c 
                                                             0 
                                                             
                                                              
                                                             cos 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             α 
                                                             
                                                             
                                                             ) 
                                                           
                                                         
                                                         + 
                                                         
                                                           
                                                             m 
                                                             aw1n 
                                                           
                                                            
                                                           
                                                             sin 
                                                              
                                                             
                                                             ( 
                                                             
                                                             α 
                                                             + 
                                                             
                                                             γ 
                                                             n 
                                                             
                                                             + 
                                                             
                                                             θ 
                                                             n 
                                                             
                                                             
                                                             ) 
                                                             
                                                           
                                                         
                                                         + 
                                                         
                                                           
                                                             z 
                                                             
                                                             6 
                                                              
                                                             n 
                                                             
                                                           
                                                            
                                                           
                                                             m 
                                                             sn 
                                                           
                                                            
                                                           
                                                             cos 
                                                              
                                                             
                                                             ( 
                                                             
                                                              
                                                             
                                                             α 
                                                             + 
                                                             
                                                             γ 
                                                             n 
                                                             
                                                             + 
                                                             
                                                             η 
                                                             n 
                                                             
                                                             
                                                             
                                                             ) 
                                                             
                                                           
                                                         
                                                         + 
                                                         
                                                           
                                                             m 
                                                             sawcn 
                                                           
                                                            
                                                           
                                                             cos 
                                                              
                                                             
                                                             ( 
                                                             
                                                             α 
                                                             + 
                                                             
                                                             γ 
                                                             n 
                                                             
                                                             
                                                             ) 
                                                             
                                                           
                                                         
                                                         + 
                                                         
                                                           
                                                             m 
                                                             sawbn 
                                                           
                                                            
                                                           sin 
                                                            
                                                           
                                                               
                                                           
                                                            
                                                           α 
                                                         
                                                       
                                                       } 
                                                     
                                                      
                                                     cos 
                                                      
                                                     
                                                         
                                                     
                                                      
                                                     β 
                                                   
                                                   - 
                                                   
                                                     ( 
                                                     
                                                       
                                                         m 
                                                         ba 
                                                       
                                                       + 
                                                       
                                                         
                                                           m 
                                                           sawan 
                                                         
                                                          
                                                         sin 
                                                          
                                                         
                                                             
                                                         
                                                          
                                                         β 
                                                       
                                                     
                                                     ) 
                                                   
                                                 
                                               
                                             
                                           
                                         
                                       
                                     
                                   
                                 
                                 ] 
                               
                               + 
                               
                                 
                                   α 
                                   . 
                                 
                                  
                                 
                                   
                                     z 
                                     . 
                                   
                                   0 
                                 
                                  
                                 
                                   m 
                                   b 
                                 
                                  
                                 sin 
                                  
                                 
                                     
                                 
                                  
                                 
                                   β 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           b 
                                           0 
                                         
                                          
                                         cos 
                                          
                                         
                                             
                                         
                                          
                                         α 
                                       
                                       - 
                                       
                                         
                                           c 
                                           0 
                                         
                                          
                                         sin 
                                          
                                         
                                             
                                         
                                          
                                         α 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               - 
                               
                                 
                                   β 
                                   . 
                                 
                                  
                                 
                                   
                                     z 
                                     . 
                                   
                                   0 
                                 
                                  
                                 
                                   { 
                                   
                                     
                                       
                                         m 
                                         ba 
                                       
                                        
                                       sin 
                                        
                                       
                                           
                                       
                                        
                                       β 
                                     
                                     - 
                                     
                                       
                                         
                                           m 
                                           b 
                                         
                                          
                                         
                                           ( 
                                           
                                             
                                               
                                                 b 
                                                 0 
                                               
                                                
                                               sin 
                                                
                                               
                                                   
                                               
                                                
                                               α 
                                             
                                             + 
                                             
                                               
                                                 c 
                                                 0 
                                               
                                                
                                               cos 
                                                
                                               
                                                   
                                               
                                                
                                               α 
                                             
                                           
                                           ) 
                                         
                                       
                                        
                                       cos 
                                        
                                       
                                           
                                       
                                        
                                       β 
                                     
                                   
                                   } 
                                 
                               
                               - 
                               
                                 g 
                                  
                                 
                                     
                                 
                                  
                                 
                                   m 
                                   ba 
                                 
                                  
                                 cos 
                                  
                                 
                                     
                                 
                                  
                                 β 
                               
                               + 
                               
                                 
                                   
                                     m 
                                     b 
                                   
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           b 
                                           0 
                                         
                                          
                                         sin 
                                          
                                         
                                             
                                         
                                          
                                         α 
                                       
                                       + 
                                       
                                         
                                           c 
                                           0 
                                         
                                          
                                         cos 
                                          
                                         
                                             
                                         
                                          
                                         α 
                                       
                                     
                                     ) 
                                   
                                 
                                  
                                 sin 
                                  
                                 
                                     
                                 
                                  
                                 β 
                               
                             
                             } 
                           
                           - 
                           
                             〈 
                             
                               
                                 g 
                                  
                                 
                                   [ 
                                   
                                     
                                       
                                         { 
                                         
                                           
                                             
                                               m 
                                               sn 
                                             
                                              
                                             
                                               z 
                                               
                                                 6 
                                                  
                                                 n 
                                               
                                             
                                              
                                             
                                               cos 
                                                
                                               
                                                 ( 
                                                 
                                                   α 
                                                   + 
                                                   
                                                     γ 
                                                     n 
                                                   
                                                   + 
                                                   
                                                     η 
                                                     n 
                                                   
                                                 
                                                 ) 
                                               
                                             
                                           
                                           + 
                                           
                                             
                                               m 
                                               aw1n 
                                             
                                              
                                             
                                               sin 
                                                
                                               
                                                 ( 
                                                 
                                                   α 
                                                   + 
                                                   
                                                     γ 
                                                     n 
                                                   
                                                   + 
                                                   
                                                     θ 
                                                     n 
                                                   
                                                 
                                                 ) 
                                               
                                             
                                           
                                           + 
                                           
                                             
                                               m 
                                               sawcn 
                                             
                                              
                                             
                                               cos 
                                                
                                               
                                                 ( 
                                                 
                                                   α 
                                                   + 
                                                   
                                                     γ 
                                                     n 
                                                   
                                                 
                                                 ) 
                                               
                                             
                                           
                                           + 
                                           
                                             
                                               m 
                                               sawbn 
                                             
                                              
                                             sin 
                                              
                                             
                                                 
                                             
                                              
                                             α 
                                           
                                         
                                         } 
                                       
                                        
                                       sin 
                                        
                                       
                                           
                                       
                                        
                                       β 
                                     
                                     + 
                                     
                                       
                                         m 
                                         sawan 
                                       
                                        
                                       cos 
                                        
                                       
                                           
                                       
                                        
                                       β 
                                     
                                   
                                   ] 
                                 
                               
                               - 
                               
                                 
                                   
                                     z 
                                     . 
                                   
                                   0 
                                 
                                  
                                 
                                   { 
                                   
                                     
                                       
                                         
                                           z 
                                           . 
                                         
                                         
                                           6 
                                            
                                           n 
                                         
                                       
                                        
                                       
                                         m 
                                         sn 
                                       
                                        
                                       
                                         cos 
                                          
                                         
                                           ( 
                                           
                                             α 
                                             + 
                                             
                                               γ 
                                               n 
                                             
                                             + 
                                             
                                               η 
                                               n 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                     + 
                                     
                                       
                                         ( 
                                         
                                           
                                             α 
                                             . 
                                           
                                           + 
                                           
                                             
                                               θ 
                                               . 
                                             
                                             n 
                                           
                                         
                                         ) 
                                       
                                        
                                       
                                         m 
                                         aw1n 
                                       
                                        
                                       
                                         cos 
                                          
                                         
                                           ( 
                                           
                                             α 
                                             + 
                                             
                                               γ 
                                               n 
                                             
                                             + 
                                             
                                               θ 
                                               n 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                     - 
                                     
                                       
                                         ( 
                                         
                                           
                                             α 
                                             . 
                                           
                                           + 
                                           
                                             
                                               η 
                                               . 
                                             
                                             n 
                                           
                                         
                                         ) 
                                       
                                        
                                       
                                         z 
                                         
                                           6 
                                            
                                           n 
                                         
                                       
                                        
                                       
                                         m 
                                         sn 
                                       
                                        
                                       
                                         sin 
                                          
                                         
                                           ( 
                                           
                                             α 
                                             + 
                                             
                                               γ 
                                               n 
                                             
                                             + 
                                             
                                               η 
                                               n 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                     - 
                                     
                                       
                                         α 
                                         . 
                                       
                                        
                                       
                                         m 
                                         sawcn 
                                       
                                        
                                       
                                         sin 
                                          
                                         
                                           ( 
                                           
                                             α 
                                             + 
                                             
                                               γ 
                                               n 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                     + 
                                     
                                       
                                         α 
                                         . 
                                       
                                        
                                       
                                         m 
                                         sawbn 
                                       
                                        
                                       cos 
                                        
                                       
                                           
                                       
                                        
                                       α 
                                     
                                     - 
                                     
                                       
                                         β 
                                         . 
                                       
                                        
                                       
                                         m 
                                         sawan 
                                       
                                     
                                   
                                   } 
                                 
                                  
                                 sin 
                                  
                                 
                                     
                                 
                                  
                                 β 
                               
                             
                           
                         
                         } 
                       
                       - 
                       
                         
                           β 
                           . 
                         
                          
                         
                           
                             z 
                             . 
                           
                           0 
                         
                          
                         
                           { 
                           
                             
                               
                                 m 
                                 aw1n 
                               
                                
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     α 
                                     + 
                                     
                                       γ 
                                       n 
                                     
                                     + 
                                     
                                       θ 
                                       n 
                                     
                                   
                                   ) 
                                 
                               
                             
                             + 
                             
                               
                                 z 
                                 
                                   6 
                                    
                                   n 
                                 
                               
                                
                               
                                 m 
                                 sn 
                               
                                
                               
                                 cos 
                                  
                                 
                                   ( 
                                   
                                     α 
                                     + 
                                     
                                       γ 
                                       n 
                                     
                                     + 
                                     
                                       η 
                                       n 
                                     
                                   
                                   ) 
                                 
                               
                             
                             + 
                             
                               
                                 m 
                                 sawcn 
                               
                                
                               
                                 cos 
                                  
                                 
                                   ( 
                                   
                                     α 
                                     + 
                                     
                                       γ 
                                       n 
                                     
                                   
                                   ) 
                                 
                               
                             
                             + 
                             
                               
                                 m 
                                 sawbn 
                               
                                
                               sin 
                                
                               
                                   
                               
                                
                               α 
                             
                           
                           } 
                         
                          
                         cos 
                          
                         
                             
                         
                          
                         β 
                       
                     
                     〉 
                   
                   = 
                   
                      
                     
                       
                         λ 
                         
                           3 
                            
                           n 
                         
                       
                       [ 
                       
                         
                           
                             
                               
                                 - 
                                 
                                   { 
                                   
                                     
                                       
                                         z 
                                         
                                           12 
                                            
                                           n 
                                         
                                       
                                        
                                       cos 
                                        
                                       
                                           
                                       
                                        
                                       α 
                                     
                                     + 
                                     
                                       
                                         e 
                                         
                                           3 
                                            
                                           n 
                                         
                                       
                                        
                                       
                                         sin 
                                          
                                         
                                           ( 
                                           
                                             α 
                                             + 
                                             
                                               γ 
                                               
                                                 n 
                                                  
                                                 
                                                     
                                                 
                                               
                                             
                                             + 
                                             
                                               θ 
                                               n 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                     + 
                                     
                                       
                                         c 
                                         
                                           2 
                                            
                                           n 
                                         
                                       
                                        
                                       
                                         cos 
                                          
                                         
                                           ( 
                                           
                                             α 
                                             + 
                                             
                                               γ 
                                               n 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                     + 
                                     
                                        
                                       
                                         
                                           b 
                                           
                                             2 
                                              
                                             n 
                                           
                                         
                                          
                                         sin 
                                          
                                         
                                             
                                         
                                          
                                         α 
                                       
                                     
                                   
                                 
                               
                               } 
                             
                              
                             
                                
                               
                                 
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   β 
                                 
                                 + 
                                 
                                    
                                   
                                     
                                       a 
                                       
                                         1 
                                          
                                         n 
                                       
                                     
                                      
                                     cos 
                                      
                                     
                                         
                                     
                                      
                                     β 
                                   
                                 
                               
                             
                           
                           ] 
                         
                          
                         
                            
                            
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5.90 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         β 
                         ¨ 
                       
                        
                       
                         ( 
                         
                           
                             m 
                             saw2n 
                           
                           + 
                           
                             m 
                             baI 
                           
                           + 
                           
                             
                               m 
                               b 
                             
                              
                             
                               A 
                               1 
                               2 
                             
                           
                           + 
                           
                             
                               m 
                               sn 
                             
                              
                             
                               B 
                               1 
                               2 
                             
                           
                           + 
                           
                             
                               m 
                               an 
                             
                              
                             
                               B 
                               2 
                               2 
                             
                           
                           + 
                           
                             
                               m 
                               wn 
                             
                              
                             
                               B 
                               3 
                               2 
                             
                           
                         
                         ) 
                       
                     
                     + 
                     
                       2 
                        
                       
                         
                           β 
                           . 
                         
                          
                         
                           [ 
                           
                             
                               
                                 α 
                                 . 
                               
                                
                               
                                 m 
                                 b 
                               
                                
                               
                                 A 
                                 1 
                               
                                
                               
                                 A 
                                 2 
                               
                             
                             + 
                             
                               
                                 m 
                                 sn 
                               
                                
                               
                                 B 
                                 1 
                               
                                
                               
                                 { 
                                 
                                   
                                     
                                       
                                         z 
                                         . 
                                       
                                       
                                         6 
                                          
                                         n 
                                       
                                     
                                      
                                     
                                       C 
                                       
                                         αγη 
                                          
                                         
                                             
                                         
                                          
                                         n 
                                       
                                     
                                   
                                   - 
                                   
                                     
                                       ( 
                                       
                                         
                                           α 
                                           . 
                                         
                                         + 
                                         
                                           
                                             η 
                                             . 
                                           
                                           n 
                                         
                                       
                                       ) 
                                     
                                      
                                     
                                       z 
                                       
                                         6 
                                          
                                         n 
                                       
                                     
                                      
                                     
                                       S 
                                       
                                         αγη 
                                          
                                         
                                             
                                         
                                          
                                         n 
                                       
                                     
                                   
                                   - 
                                   
                                     
                                       α 
                                       . 
                                     
                                      
                                     
                                       A 
                                       4 
                                     
                                   
                                 
                                 } 
                               
                             
                             + 
                             
                               
                                 m 
                                 
                                   an 
                                    
                                   
                                       
                                   
                                 
                               
                                
                               
                                 B 
                                 2 
                               
                                
                               
                                 { 
                                 
                                   
                                     
                                       ( 
                                       
                                         
                                           α 
                                           . 
                                         
                                         + 
                                         
                                           
                                             θ 
                                             . 
                                           
                                           n 
                                         
                                       
                                       ) 
                                     
                                      
                                     
                                       e 
                                       
                                         1 
                                          
                                         n 
                                       
                                     
                                      
                                     
                                       C 
                                       
                                         αγθ 
                                          
                                         
                                             
                                         
                                          
                                         n 
                                       
                                     
                                   
                                   - 
                                   
                                     
                                       α 
                                       . 
                                     
                                      
                                     
                                       A 
                                       6 
                                     
                                   
                                 
                                 } 
                               
                             
                             + 
                             
                               
                                 m 
                                 wn 
                               
                                
                               
                                 B 
                                 3 
                               
                                
                               
                                 { 
                                 
                                   
                                     
                                       ( 
                                       
                                         
                                           α 
                                           . 
                                         
                                         + 
                                         
                                           
                                             θ 
                                             . 
                                           
                                           n 
                                         
                                       
                                       ) 
                                     
                                      
                                     
                                       e 
                                       
                                         3 
                                          
                                         n 
                                       
                                     
                                      
                                     
                                       S 
                                       
                                         αγθ 
                                          
                                         
                                             
                                         
                                          
                                         n 
                                       
                                     
                                   
                                   - 
                                   
                                     
                                       α 
                                       . 
                                     
                                      
                                     
                                       A 
                                       6 
                                     
                                   
                                 
                                 } 
                               
                             
                           
                           ] 
                         
                       
                     
                     - 
                     
                       
                         α 
                         ¨ 
                       
                        
                       
                         m 
                         ba 
                       
                        
                       
                         A 
                         2 
                       
                     
                     + 
                     
                       
                         
                           α 
                           . 
                         
                         2 
                       
                        
                       
                         m 
                         ba 
                       
                        
                       
                         A 
                         1 
                       
                     
                     - 
                     
                       
                         
                           z 
                           ¨ 
                         
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         a 
                         
                           1 
                            
                           n 
                         
                       
                        
                       
                         C 
                         
                           αγη 
                            
                           
                               
                           
                            
                           n 
                         
                       
                     
                     + 
                     
                       2 
                        
                       
                           
                       
                        
                       
                         
                           
                             z 
                             . 
                           
                           
                             6 
                              
                             n 
                           
                         
                          
                         
                           ( 
                           
                             
                               α 
                               . 
                             
                             + 
                             
                               
                                 η 
                                 . 
                               
                               n 
                             
                           
                           ) 
                         
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         a 
                         
                           1 
                            
                           n 
                         
                       
                        
                       
                         S 
                         
                           αγη 
                            
                           
                               
                           
                            
                           n 
                         
                       
                     
                     + 
                     
                       
                         
                           η 
                           ¨ 
                         
                         n 
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         z 
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         a 
                         
                           1 
                            
                           n 
                         
                       
                        
                       
                         S 
                         
                           αγη 
                            
                           
                               
                           
                            
                           n 
                         
                       
                     
                     + 
                     
                       
                         
                           
                             η 
                             . 
                           
                           n 
                         
                          
                         
                           ( 
                           
                             
                               2 
                                
                               
                                 α 
                                 . 
                               
                             
                             + 
                             
                               
                                 η 
                                 . 
                               
                               n 
                             
                           
                           ) 
                         
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         z 
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         a 
                         
                           1 
                            
                           n 
                         
                       
                        
                       
                         C 
                         
                           αγη 
                            
                           
                               
                           
                            
                           n 
                         
                       
                     
                     - 
                     
                       
                         
                           θ 
                           ¨ 
                         
                         n 
                       
                        
                       
                         m 
                         aw1n 
                       
                        
                       
                         a 
                         
                           1 
                            
                           n 
                         
                       
                        
                       
                         C 
                         
                           αγθ 
                            
                           
                               
                           
                            
                           n 
                         
                       
                     
                     + 
                     
                       
                         
                           
                             θ 
                             . 
                           
                           n 
                         
                          
                         
                           ( 
                           
                             
                               2 
                                
                               
                                 α 
                                 . 
                               
                             
                             + 
                             
                               
                                 θ 
                                 . 
                               
                               n 
                             
                           
                           ) 
                         
                       
                        
                       
                         m 
                         aw1n 
                       
                        
                       
                         a 
                         
                           1 
                            
                           n 
                         
                       
                        
                       
                         S 
                         
                           αγθ 
                            
                           
                               
                           
                            
                           n 
                         
                       
                     
                     + 
                     
                       
                         α 
                         ¨ 
                       
                        
                       
                         a 
                         
                           1 
                            
                           n 
                         
                       
                        
                       
                         { 
                         
                           
                             
                               m 
                               sawcn 
                             
                              
                             
                               S 
                               
                                 αγ 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                           
                           - 
                           
                             
                               m 
                               sawbn 
                             
                              
                             
                               C 
                               α 
                             
                           
                           + 
                           
                             
                               m 
                               sn 
                             
                              
                             
                               z 
                               
                                 6 
                                  
                                 n 
                               
                             
                              
                             
                               S 
                               
                                 αγη 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                           
                           - 
                           
                             
                               m 
                               aw1n 
                             
                              
                             
                               C 
                               
                                 αγθ 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                           
                         
                         } 
                       
                     
                     + 
                     
                       
                         
                           α 
                           . 
                         
                         2 
                       
                        
                       
                         a 
                         
                           1 
                            
                           n 
                         
                       
                        
                       
                         { 
                         
                           
                             
                               m 
                               sawcn 
                             
                              
                             
                               C 
                               
                                 αγ 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                           
                           + 
                           
                             
                               m 
                               sawbn 
                             
                              
                             
                               S 
                               α 
                             
                           
                           + 
                           
                             
                               m 
                               sn 
                             
                              
                             
                               z 
                               
                                 6 
                                  
                                 n 
                               
                             
                              
                             
                               C 
                               
                                 αγη 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                           
                           + 
                           
                             
                               m 
                               aw1n 
                             
                              
                             
                               S 
                               
                                 αγθ 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                           
                         
                         } 
                       
                     
                     - 
                     
                       
                         
                           z 
                           ¨ 
                         
                         0 
                       
                        
                       
                         [ 
                         
                           
                             
                               { 
                               
                                 
                                   
                                     m 
                                     b 
                                   
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           b 
                                           0 
                                         
                                          
                                         
                                           S 
                                           α 
                                         
                                       
                                       + 
                                       
                                         
                                           c 
                                           0 
                                         
                                          
                                         
                                           C 
                                           α 
                                         
                                       
                                     
                                     ) 
                                   
                                 
                                 + 
                                 
                                   
                                     m 
                                     aw1n 
                                   
                                    
                                   
                                     S 
                                     
                                       αγη 
                                        
                                       
                                           
                                       
                                        
                                       n 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     z 
                                     
                                       6 
                                        
                                       n 
                                     
                                   
                                    
                                   
                                     m 
                                     sn 
                                   
                                    
                                   
                                     C 
                                     
                                       αγη 
                                        
                                       
                                           
                                       
                                        
                                       n 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     m 
                                     sawcn 
                                   
                                    
                                   
                                     C 
                                     
                                       αγ 
                                        
                                       
                                           
                                       
                                        
                                       n 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     m 
                                     sawbn 
                                   
                                    
                                   
                                     S 
                                     α 
                                   
                                 
                               
                               } 
                             
                              
                             
                               S 
                               β 
                             
                           
                           + 
                           
                             
                               ( 
                               
                                 
                                   m 
                                   ba 
                                 
                                 + 
                                 
                                   m 
                                   sawan 
                                 
                               
                               ) 
                             
                              
                             
                               C 
                               β 
                             
                           
                         
                         ] 
                       
                     
                     + 
                     
                       
                         
                           
                             z 
                             . 
                           
                           0 
                         
                          
                         
                           ( 
                           
                             1 
                             - 
                             
                               β 
                               . 
                             
                           
                           ) 
                         
                       
                        
                       
                         ( 
                         
                           
                             m 
                             ba 
                           
                           + 
                           
                             m 
                             sawan 
                           
                         
                         ) 
                       
                        
                       sin 
                        
                       
                           
                       
                        
                       β 
                     
                     - 
                     
                       g 
                        
                       
                         [ 
                         
                           
                             
                               m 
                               ba 
                             
                              
                             
                               C 
                               β 
                             
                           
                           + 
                           
                             
                               m 
                               b 
                             
                              
                             
                               A 
                               1 
                             
                              
                             
                               S 
                               β 
                             
                           
                           + 
                           
                             
                               { 
                               
                                 
                                   
                                     m 
                                     sn 
                                   
                                    
                                   
                                     z 
                                     
                                       6 
                                        
                                       n 
                                     
                                   
                                    
                                   
                                     C 
                                     
                                       αγη 
                                        
                                       
                                           
                                       
                                        
                                       n 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     m 
                                     aw1n 
                                   
                                    
                                   
                                     S 
                                     
                                       αγθ 
                                        
                                       
                                           
                                       
                                        
                                       n 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     m 
                                     sawcn 
                                   
                                    
                                   
                                     C 
                                     
                                       αγ 
                                        
                                       
                                           
                                       
                                        
                                       n 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     m 
                                     sawbn 
                                   
                                    
                                   
                                     S 
                                     α 
                                   
                                 
                               
                               } 
                             
                              
                             
                               S 
                               β 
                             
                           
                           + 
                           
                             
                               m 
                               sawan 
                             
                              
                             
                               C 
                               β 
                             
                           
                         
                         ] 
                       
                     
                   
                   = 
                   
                     
                       λ 
                       
                         3 
                          
                         n 
                       
                     
                      
                     
                       [ 
                       
                         
                           
                             - 
                             
                               { 
                               
                                 
                                   
                                     z 
                                     
                                       12 
                                        
                                       n 
                                     
                                   
                                    
                                   
                                     C 
                                     α 
                                   
                                 
                                 + 
                                 
                                   
                                     e 
                                     
                                       3 
                                        
                                       n 
                                     
                                   
                                    
                                   
                                     S 
                                     
                                       αγθ 
                                        
                                       
                                           
                                       
                                        
                                       n 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     c 
                                     
                                       2 
                                        
                                       n 
                                     
                                   
                                    
                                   
                                     C 
                                     
                                       αγ 
                                        
                                       
                                           
                                       
                                        
                                       n 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     b 
                                     
                                       2 
                                        
                                       n 
                                     
                                   
                                    
                                   
                                     S 
                                     α 
                                   
                                 
                               
                               } 
                             
                           
                            
                           
                             S 
                             β 
                           
                         
                         + 
                         
                           
                             a 
                             
                               1 
                                
                               n 
                             
                           
                            
                           
                             C 
                             β 
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   5.91 
                   ) 
                 
               
             
             
               
                 
                   
                     β 
                     ¨ 
                   
                   = 
                   
                       
                   
                    
                   
                     
                       
                           
                       
                        
                       
                         
                           2 
                            
                           
                             
                               β 
                               . 
                             
                              
                             
                               [ 
                               
                                 
                                   
                                     α 
                                     . 
                                   
                                    
                                   
                                     m 
                                     b 
                                   
                                    
                                   
                                     A 
                                     1 
                                   
                                    
                                   
                                     A 
                                     2 
                                   
                                 
                                 + 
                                 
                                   
                                     m 
                                     sn 
                                   
                                    
                                   
                                     B 
                                     1 
                                   
                                    
                                   
                                     { 
                                     
                                       
                                         
                                           
                                             z 
                                             . 
                                           
                                           
                                             6 
                                              
                                             n 
                                           
                                         
                                          
                                         
                                           C 
                                           
                                             αγη 
                                              
                                             
                                                 
                                             
                                              
                                             n 
                                           
                                         
                                       
                                       - 
                                       
                                         
                                           ( 
                                           
                                             
                                               α 
                                               . 
                                             
                                             + 
                                             
                                               
                                                 η 
                                                 . 
                                               
                                               n 
                                             
                                           
                                           ) 
                                         
                                          
                                         
                                           z 
                                           
                                             6 
                                              
                                             n 
                                           
                                         
                                          
                                         
                                           S 
                                           
                                             αγη 
                                              
                                             
                                                 
                                             
                                              
                                             n 
                                           
                                         
                                       
                                       - 
                                       
                                         
                                           α 
                                           . 
                                         
                                          
                                         
                                           A 
                                           4 
                                         
                                       
                                     
                                     } 
                                   
                                 
                                 + 
                                 
                                   
                                     m 
                                     an 
                                   
                                    
                                   
                                     B 
                                     2 
                                   
                                    
                                   
                                     { 
                                     
                                       
                                         
                                           ( 
                                           
                                             
                                               α 
                                               . 
                                             
                                             + 
                                             
                                               
                                                 θ 
                                                 . 
                                               
                                               n 
                                             
                                           
                                           ) 
                                         
                                          
                                         
                                           e 
                                           
                                             1 
                                              
                                             n 
                                           
                                         
                                          
                                         
                                           C 
                                           
                                             αγθ 
                                              
                                             
                                                 
                                             
                                              
                                             n 
                                           
                                         
                                       
                                       - 
                                       
                                         
                                           α 
                                           . 
                                         
                                          
                                         
                                           A 
                                           6 
                                         
                                       
                                     
                                     } 
                                   
                                 
                                 + 
                                 
                                   
 
                                 
                                  
                                 
                                   
                                     m 
                                     wn 
                                   
                                    
                                   
                                     B 
                                     3 
                                   
                                    
                                   
                                     { 
                                     
                                       
                                         
                                           ( 
                                           
                                             
                                               α 
                                               . 
                                             
                                             + 
                                             
                                               
                                                 θ 
                                                 . 
                                               
                                               n 
                                             
                                           
                                           ) 
                                         
                                          
                                         
                                           e 
                                           
                                             3 
                                              
                                             n 
                                           
                                         
                                          
                                         
                                           S 
                                           
                                             αγθ 
                                              
                                             
                                                 
                                             
                                              
                                             n 
                                           
                                         
                                       
                                       - 
                                       
                                         
                                           α 
                                           . 
                                         
                                          
                                         
                                           A 
                                           6 
                                         
                                       
                                     
                                     } 
                                   
                                 
                               
                               ] 
                             
                           
                         
                         - 
                         
                           
                             α 
                             ¨ 
                           
                            
                           
                             m 
                             ba 
                           
                            
                           
                             A 
                             2 
                           
                         
                         + 
                         
                           
                             
                               α 
                               . 
                             
                             2 
                           
                            
                           
                             m 
                             ba 
                           
                            
                           
                             A 
                             1 
                           
                         
                         - 
                         
                           
                             
                               z 
                               ¨ 
                             
                             
                               6 
                                
                               n 
                             
                           
                            
                           
                             m 
                             sn 
                           
                            
                           
                             a 
                             
                               1 
                                
                               n 
                             
                           
                            
                           
                             C 
                             
                               αγη 
                                
                               
                                   
                               
                                
                               n 
                             
                           
                         
                         + 
                         
                           2 
                            
                           
                             
                               
                                 z 
                                 . 
                               
                               
                                 6 
                                  
                                 n 
                               
                             
                              
                             
                               ( 
                               
                                 
                                   α 
                                   . 
                                 
                                 + 
                                 
                                   
                                     η 
                                     . 
                                   
                                   n 
                                 
                               
                               ) 
                             
                           
                            
                           
                             m 
                             sn 
                           
                            
                           
                             a 
                             
                               1 
                                
                               n 
                             
                           
                            
                           
                             S 
                             
                               αγη 
                                
                               
                                   
                               
                                
                               n 
                             
                           
                         
                         + 
                         
                           
 
                         
                          
                         
                             
                         
                          
                         
                           
                             
                               η 
                               ¨ 
                             
                             n 
                           
                            
                           
                             m 
                             sn 
                           
                            
                           
                             z 
                             
                               6 
                                
                               n 
                             
                           
                            
                           
                             a 
                             
                               1 
                                
                               n 
                             
                           
                            
                           
                             S 
                             
                               αγη 
                                
                               
                                   
                               
                                
                               n 
                             
                           
                         
                         + 
                         
                           
                             
                               
                                 η 
                                 . 
                               
                               n 
                             
                              
                             
                               ( 
                               
                                 
                                   2 
                                    
                                   
                                     α 
                                     . 
                                   
                                 
                                 + 
                                 
                                   
                                     η 
                                     . 
                                   
                                   n 
                                 
                               
                               ) 
                             
                           
                            
                           
                             m 
                             sn 
                           
                            
                           
                             z 
                             
                               6 
                                
                               n 
                             
                           
                            
                           
                             a 
                             
                               1 
                                
                               n 
                             
                           
                            
                           
                             C 
                             
                               αγη 
                                
                               
                                   
                               
                                
                               n 
                             
                           
                         
                         - 
                         
                           
                             
                               θ 
                               ¨ 
                             
                             n 
                           
                            
                           
                             m 
                             aw1n 
                           
                            
                           
                             a 
                             
                               1 
                                
                               n 
                             
                           
                            
                           
                             C 
                             
                               αγθ 
                                
                               
                                   
                               
                                
                               n 
                             
                           
                         
                         + 
                         
                           
                             
                               
                                 θ 
                                 . 
                               
                               n 
                             
                              
                             
                               ( 
                               
                                 
                                   2 
                                    
                                   
                                       
                                   
                                    
                                   
                                     α 
                                     . 
                                   
                                 
                                 + 
                                 
                                   
                                     θ 
                                     . 
                                   
                                   n 
                                 
                               
                               ) 
                             
                           
                            
                           
                             m 
                             aw1n 
                           
                            
                           
                             a 
                             
                               1 
                                
                               n 
                             
                           
                            
                           
                             S 
                             
                               αγθ 
                                
                               
                                   
                               
                                
                               n 
                             
                           
                         
                         + 
                         
                           
 
                         
                          
                         
                             
                         
                          
                         
                           
                             α 
                             ¨ 
                           
                            
                           
                             a 
                             
                               1 
                                
                               n 
                             
                           
                            
                           
                             { 
                             
                               
                                 
                                   m 
                                   sawcn 
                                 
                                  
                                 
                                   S 
                                   
                                     αγ 
                                      
                                     
                                         
                                     
                                      
                                     n 
                                   
                                 
                               
                               - 
                               
                                 
                                   m 
                                   sawbn 
                                 
                                  
                                 
                                   C 
                                   α 
                                 
                               
                               + 
                               
                                 
                                   m 
                                   sn 
                                 
                                  
                                 
                                   z 
                                   
                                     6 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   S 
                                   
                                     αγη 
                                      
                                     
                                         
                                     
                                      
                                     n 
                                   
                                 
                               
                               - 
                               
                                 
                                   m 
                                   aw1n 
                                 
                                  
                                 
                                   C 
                                   
                                     αγθ 
                                      
                                     
                                         
                                     
                                      
                                     n 
                                   
                                 
                               
                             
                             } 
                           
                         
                         + 
                         
                           
 
                         
                          
                         
                             
                         
                          
                         
                           
                             
                               α 
                               . 
                             
                             2 
                           
                            
                           
                             a 
                             
                               1 
                                
                               n 
                             
                           
                            
                           
                             { 
                             
                               
                                 
                                   m 
                                   sawcn 
                                 
                                  
                                 
                                   C 
                                   
                                     αγ 
                                      
                                     
                                         
                                     
                                      
                                     n 
                                   
                                 
                               
                               + 
                               
                                 
                                   m 
                                   sawbn 
                                 
                                  
                                 
                                   S 
                                   α 
                                 
                               
                               + 
                               
                                 
                                   m 
                                   sn 
                                 
                                  
                                 
                                   z 
                                   
                                     6 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   C 
                                   
                                     αγη 
                                      
                                     
                                         
                                     
                                      
                                     n 
                                   
                                 
                               
                               + 
                               
                                 
                                   m 
                                   aw1n 
                                 
                                  
                                 
                                   S 
                                   
                                     αγθ 
                                      
                                     
                                         
                                     
                                      
                                     n 
                                   
                                 
                               
                             
                             } 
                           
                         
                         - 
                         
                           
 
                         
                          
                         
                             
                         
                          
                         
                           
                             
                               z 
                               ¨ 
                             
                             0 
                           
                            
                           
                             [ 
                             
                               
                                 
                                   { 
                                   
                                     
                                       
                                         m 
                                         b 
                                       
                                        
                                       
                                         ( 
                                         
                                           
                                             
                                               b 
                                               0 
                                             
                                              
                                             
                                               S 
                                               α 
                                             
                                           
                                           + 
                                           
                                             
                                               c 
                                               0 
                                             
                                              
                                             
                                               C 
                                               α 
                                             
                                           
                                         
                                         ) 
                                       
                                     
                                     + 
                                     
                                       
                                         m 
                                         aw1n 
                                       
                                        
                                       
                                         S 
                                         
                                           αγη 
                                            
                                           
                                               
                                           
                                            
                                           n 
                                         
                                       
                                     
                                     + 
                                     
                                       
                                         z 
                                         
                                           6 
                                            
                                           n 
                                         
                                       
                                        
                                       
                                         m 
                                         sn 
                                       
                                        
                                       
                                         C 
                                         
                                           αγη 
                                            
                                           
                                               
                                           
                                            
                                           n 
                                         
                                       
                                     
                                     + 
                                     
                                       
                                         m 
                                         sawcn 
                                       
                                        
                                       
                                         C 
                                         
                                           αγ 
                                            
                                           
                                               
                                           
                                            
                                           n 
                                         
                                       
                                     
                                     + 
                                     
                                       
 
                                     
                                      
                                     
                                         
                                     
                                      
                                     
                                       
                                         m 
                                         sawbn 
                                       
                                        
                                       
                                         S 
                                         α 
                                       
                                     
                                   
                                   } 
                                 
                                  
                                 
                                   S 
                                   β 
                                 
                               
                               + 
                               
                                 
                                   ( 
                                   
                                     
                                       m 
                                       ba 
                                     
                                     + 
                                     
                                       m 
                                       sawan 
                                     
                                   
                                   ) 
                                 
                                  
                                 
                                   C 
                                   β 
                                 
                               
                             
                             ] 
                           
                         
                         + 
                         
                           
                             
                               
                                 z 
                                 . 
                               
                               0 
                             
                              
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   β 
                                   . 
                                 
                               
                               ) 
                             
                           
                            
                           
                             ( 
                             
                               
                                 m 
                                 ba 
                               
                               + 
                               
                                 m 
                                 sawan 
                               
                             
                             ) 
                           
                            
                           sin 
                            
                           
                               
                           
                            
                           β 
                         
                         - 
                         
                           
 
                         
                          
                         
                             
                         
                          
                         
                           g 
                            
                           
                             [ 
                             
                               
                                 
                                   m 
                                   ba 
                                 
                                  
                                 
                                   C 
                                   β 
                                 
                               
                               + 
                               
                                 
                                   m 
                                   b 
                                 
                                  
                                 
                                   A 
                                   1 
                                 
                                  
                                 
                                   S 
                                   β 
                                 
                               
                               + 
                               
                                 
                                   { 
                                   
                                     
                                       
                                         m 
                                         sn 
                                       
                                        
                                       
                                         z 
                                         
                                           6 
                                            
                                           n 
                                         
                                       
                                        
                                       
                                         C 
                                         
                                           αγη 
                                            
                                           
                                               
                                           
                                            
                                           n 
                                         
                                       
                                     
                                     + 
                                     
                                       
                                         m 
                                         aw1n 
                                       
                                        
                                       
                                         S 
                                         
                                           αγθ 
                                            
                                           
                                               
                                           
                                            
                                           n 
                                         
                                       
                                     
                                     + 
                                     
                                       
                                         m 
                                         sawcn 
                                       
                                        
                                       
                                         C 
                                         
                                           αγ 
                                            
                                           
                                               
                                           
                                            
                                           n 
                                         
                                       
                                     
                                     + 
                                     
                                       
 
                                     
                                      
                                     
                                         
                                     
                                      
                                     
                                       
                                         m 
                                         sawbn 
                                       
                                        
                                       
                                         S 
                                         α 
                                       
                                     
                                   
                                   } 
                                 
                                  
                                 
                                   S 
                                   β 
                                 
                               
                               + 
                               
                                 
                                   m 
                                   sawan 
                                 
                                  
                                 
                                   C 
                                   β 
                                 
                               
                             
                             ] 
                           
                         
                         + 
                         
                           
                             λ 
                             
                               3 
                                
                               n 
                             
                           
                            
                           
                             { 
                             
                               
                                 
                                   ( 
                                   
                                     
                                       
                                         z 
                                         
                                           12 
                                            
                                           n 
                                         
                                       
                                        
                                       
                                         C 
                                         α 
                                       
                                     
                                     + 
                                     
                                       
                                         e 
                                         
                                           3 
                                            
                                           n 
                                         
                                       
                                        
                                       
                                         S 
                                         
                                           αγθ 
                                            
                                           
                                               
                                           
                                            
                                           n 
                                         
                                       
                                     
                                     + 
                                     
                                       
                                         c 
                                         
                                           2 
                                            
                                           n 
                                         
                                       
                                        
                                       
                                         C 
                                         
                                           αγ 
                                            
                                           
                                               
                                           
                                            
                                           n 
                                         
                                       
                                     
                                     + 
                                     
                                       
                                         b 
                                         
                                           2 
                                            
                                           n 
                                         
                                       
                                        
                                       
                                         S 
                                         α 
                                       
                                     
                                   
                                   ) 
                                 
                                  
                                 
                                   S 
                                   β 
                                 
                               
                               - 
                               
                                 
                                   a 
                                   
                                     1 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   C 
                                   β 
                                 
                               
                             
                             } 
                           
                         
                       
                     
                     
                       - 
                       
                         ( 
                         
                           
                             m 
                             saw2n 
                           
                           + 
                           
                             m 
                             baI 
                           
                           + 
                           
                             
                               m 
                               b 
                             
                              
                             
                               A 
                               1 
                               2 
                             
                           
                           + 
                           
                             
                               m 
                               sn 
                             
                              
                             
                               B 
                               1 
                               2 
                             
                           
                           + 
                           
                             
                               m 
                               an 
                             
                              
                             
                               B 
                               2 
                               2 
                             
                           
                           + 
                           
                             
                               m 
                               wn 
                             
                              
                             
                               B 
                               3 
                               2 
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5.92 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                            
                           
                              
                             t 
                           
                         
                          
                         
                           ( 
                           
                             
                               ∂ 
                               L 
                             
                             
                               ∂ 
                               
                                 α 
                                 . 
                               
                             
                           
                           ) 
                         
                       
                       - 
                       
                         
                           ∂ 
                           L 
                         
                         
                           ∂ 
                           α 
                         
                       
                     
                     = 
                     
                       
                         
                           
                             ∂ 
                             F 
                           
                           
                             ∂ 
                             
                               α 
                               . 
                             
                           
                         
                         + 
                         
                           
                             ∑ 
                             
                               l 
                               , 
                               n 
                             
                           
                            
                           
                             
                               λ 
                               
                                 l 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                              
                             
                               a 
                               
                                 l 
                                  
                                 
                                     
                                 
                                  
                                 n 
                                  
                                 
                                     
                                 
                                  
                                 2 
                               
                             
                              
                             
                                 
                             
                              
                             l 
                           
                         
                       
                       = 
                       1 
                     
                   
                   , 
                   2 
                   , 
                   
                     
                       3 
                        
                       
                           
                       
                        
                       n 
                     
                     = 
                     i 
                   
                   , 
                   ii 
                   , 
                   iii 
                   , 
                   iv 
                 
               
               
                 
                   ( 
                   5.93 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 
                                   
                                     
                                       
                                         
                                           
                                             
                                               - 
                                               
                                                 β 
                                                 ¨ 
                                               
                                             
                                              
                                             
                                               
                                                 m 
                                                 ba 
                                               
                                                
                                               
                                                 ( 
                                                 
                                                   
                                                     
                                                       b 
                                                       0 
                                                     
                                                      
                                                     cos 
                                                      
                                                     
                                                         
                                                     
                                                      
                                                     α 
                                                   
                                                   - 
                                                   
                                                     
                                                       c 
                                                       0 
                                                     
                                                      
                                                     sin 
                                                      
                                                     
                                                         
                                                     
                                                      
                                                     α 
                                                   
                                                 
                                                 ) 
                                               
                                             
                                           
                                           + 
                                           
                                             
                                               β 
                                               . 
                                             
                                              
                                             
                                               α 
                                               . 
                                             
                                              
                                             
                                               
                                                 m 
                                                 ba 
                                               
                                                
                                               
                                                 ( 
                                                 
                                                   
                                                     
                                                       b 
                                                       0 
                                                     
                                                      
                                                     sin 
                                                      
                                                     
                                                         
                                                     
                                                      
                                                     α 
                                                   
                                                   + 
                                                   
                                                     
                                                       c 
                                                       0 
                                                     
                                                      
                                                     cos 
                                                      
                                                     
                                                         
                                                     
                                                      
                                                     α 
                                                   
                                                 
                                                 ) 
                                               
                                             
                                           
                                           + 
                                           
                                             
                                               
                                                 z 
                                                 ¨ 
                                               
                                               0 
                                             
                                              
                                             
                                               m 
                                               b 
                                             
                                              
                                             cos 
                                              
                                             
                                                 
                                             
                                              
                                             
                                               β 
                                                
                                               
                                                 ( 
                                                 
                                                   
                                                     
                                                       b 
                                                       0 
                                                     
                                                      
                                                     cos 
                                                      
                                                     
                                                         
                                                     
                                                      
                                                     α 
                                                   
                                                   - 
                                                   
                                                     
                                                       c 
                                                       0 
                                                     
                                                      
                                                     sin 
                                                      
                                                     
                                                         
                                                     
                                                      
                                                     α 
                                                   
                                                 
                                                 ) 
                                               
                                             
                                           
                                           - 
                                           
                                             
                                               β 
                                               . 
                                             
                                              
                                             
                                               
                                                 z 
                                                 . 
                                               
                                               0 
                                             
                                              
                                             
                                               m 
                                               b 
                                             
                                              
                                             sin 
                                              
                                             
                                                 
                                             
                                              
                                             
                                               β 
                                                
                                               
                                                 ( 
                                                 
                                                   
                                                     
                                                       b 
                                                       0 
                                                     
                                                      
                                                     cos 
                                                      
                                                     
                                                         
                                                     
                                                      
                                                     α 
                                                   
                                                   - 
                                                   
                                                     
                                                       c 
                                                       0 
                                                     
                                                      
                                                     sin 
                                                      
                                                     
                                                         
                                                     
                                                      
                                                     α 
                                                   
                                                 
                                                 ) 
                                               
                                             
                                           
                                           - 
                                           
                                             
                                               α 
                                               . 
                                             
                                              
                                             
                                               
                                                 z 
                                                 . 
                                               
                                               0 
                                             
                                              
                                             
                                               m 
                                               b 
                                             
                                              
                                             cos 
                                              
                                             
                                                 
                                             
                                              
                                             
                                               β 
                                                
                                               
                                                 ( 
                                                 
                                                   
                                                     
                                                       b 
                                                       0 
                                                     
                                                      
                                                     sin 
                                                      
                                                     
                                                         
                                                     
                                                      
                                                     α 
                                                   
                                                   - 
                                                   
                                                     
                                                       c 
                                                       0 
                                                     
                                                      
                                                     cos 
                                                      
                                                     
                                                         
                                                     
                                                      
                                                     α 
                                                   
                                                 
                                                 ) 
                                               
                                             
                                           
                                           + 
                                           
                                             
                                               α 
                                               ¨ 
                                             
                                              
                                             
                                               〈 
                                               
                                                 
                                                   m 
                                                   bbI 
                                                 
                                                 + 
                                                 
                                                   m 
                                                   sawIn 
                                                 
                                                 + 
                                                 
                                                   
                                                     m 
                                                     sn 
                                                   
                                                    
                                                   
                                                     
                                                       z 
                                                       
                                                         6 
                                                          
                                                         n 
                                                       
                                                     
                                                      
                                                     
                                                       [ 
                                                       
                                                         
                                                           z 
                                                           
                                                             6 
                                                              
                                                             n 
                                                           
                                                         
                                                         + 
                                                         
                                                           2 
                                                            
                                                           
                                                             { 
                                                             
                                                             
                                                             
                                                             c 
                                                             
                                                             1 
                                                              
                                                             n 
                                                             
                                                             
                                                              
                                                             cos 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             
                                                             η 
                                                             n 
                                                             
                                                             
                                                             - 
                                                             
                                                             
                                                             b 
                                                             
                                                             2 
                                                              
                                                             n 
                                                             
                                                             
                                                              
                                                             
                                                             sin 
                                                              
                                                             
                                                             ( 
                                                             
                                                             
                                                             γ 
                                                             n 
                                                             
                                                             + 
                                                             
                                                             η 
                                                             n 
                                                             
                                                             
                                                             ) 
                                                             
                                                             
                                                             
                                                             
                                                             } 
                                                           
                                                         
                                                       
                                                       ] 
                                                     
                                                   
                                                 
                                                 - 
                                                 
                                                   2 
                                                    
                                                   
                                                     m 
                                                     aw1n 
                                                   
                                                    
                                                   
                                                     { 
                                                     
                                                       
                                                         
                                                           c 
                                                           
                                                             2 
                                                              
                                                             n 
                                                           
                                                         
                                                          
                                                         sin 
                                                          
                                                         
                                                             
                                                         
                                                          
                                                         
                                                           θ 
                                                           n 
                                                         
                                                       
                                                       - 
                                                       
                                                         
                                                           b 
                                                           
                                                             2 
                                                              
                                                             n 
                                                           
                                                         
                                                          
                                                         
                                                           cos 
                                                            
                                                           
                                                             ( 
                                                             
                                                             
                                                             γ 
                                                             n 
                                                             
                                                             + 
                                                             
                                                             θ 
                                                             n 
                                                             
                                                             
                                                             ) 
                                                           
                                                         
                                                       
                                                     
                                                     } 
                                                   
                                                 
                                               
                                               〉 
                                             
                                           
                                           + 
                                           
                                             
                                               α 
                                               . 
                                             
                                              
                                             
                                               〈 
                                               
                                                 
                                                   
                                                     m 
                                                     sn 
                                                   
                                                    
                                                   
                                                     
                                                       
                                                         z 
                                                         . 
                                                       
                                                       
                                                         6 
                                                          
                                                         n 
                                                       
                                                     
                                                      
                                                     
                                                       [ 
                                                       
                                                         
                                                           z 
                                                           
                                                             6 
                                                              
                                                             n 
                                                           
                                                         
                                                         + 
                                                         
                                                           2 
                                                            
                                                           
                                                             { 
                                                             
                                                             
                                                             
                                                             c 
                                                             
                                                             1 
                                                              
                                                             n 
                                                             
                                                             
                                                              
                                                             cos 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             
                                                             η 
                                                             n 
                                                             
                                                             
                                                             - 
                                                             
                                                             
                                                             b 
                                                             
                                                             2 
                                                              
                                                             n 
                                                             
                                                             
                                                              
                                                             
                                                             sin 
                                                              
                                                             
                                                             ( 
                                                             
                                                             
                                                             γ 
                                                             n 
                                                             
                                                             + 
                                                             
                                                             η 
                                                             n 
                                                             
                                                             
                                                             ) 
                                                             
                                                             
                                                             
                                                             
                                                             } 
                                                           
                                                         
                                                       
                                                       ] 
                                                     
                                                   
                                                 
                                                 + 
                                                 
                                                   
                                                     m 
                                                     sn 
                                                   
                                                    
                                                   
                                                     
                                                       z 
                                                       
                                                         6 
                                                          
                                                         n 
                                                       
                                                     
                                                      
                                                     
                                                       [ 
                                                       
                                                         
                                                           
                                                             z 
                                                             . 
                                                           
                                                           
                                                             6 
                                                              
                                                             n 
                                                           
                                                         
                                                         - 
                                                         
                                                           2 
                                                            
                                                           
                                                               
                                                           
                                                            
                                                           
                                                             
                                                             η 
                                                             . 
                                                             
                                                             n 
                                                           
                                                            
                                                           
                                                             { 
                                                             
                                                             
                                                             
                                                             c 
                                                             
                                                             1 
                                                              
                                                             n 
                                                             
                                                             
                                                              
                                                             sin 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             
                                                             η 
                                                             n 
                                                             
                                                             
                                                             + 
                                                             
                                                             
                                                             b 
                                                             
                                                             2 
                                                              
                                                             n 
                                                             
                                                             
                                                              
                                                             
                                                             cos 
                                                              
                                                             
                                                             ( 
                                                             
                                                             
                                                             γ 
                                                             n 
                                                             
                                                             + 
                                                             
                                                             η 
                                                             n 
                                                             
                                                             
                                                             ) 
                                                             
                                                             
                                                             
                                                             
                                                             } 
                                                           
                                                         
                                                       
                                                       ] 
                                                     
                                                   
                                                 
                                                 - 
                                                 
                                                   2 
                                                    
                                                   
                                                     
                                                       θ 
                                                       . 
                                                     
                                                     n 
                                                   
                                                    
                                                   
                                                     m 
                                                     aw1n 
                                                   
                                                    
                                                   
                                                     { 
                                                     
                                                       
                                                         
                                                           c 
                                                           
                                                             2 
                                                              
                                                             n 
                                                           
                                                         
                                                          
                                                         cos 
                                                          
                                                         
                                                             
                                                         
                                                          
                                                         
                                                           θ 
                                                           n 
                                                         
                                                       
                                                       + 
                                                       
                                                         
                                                           b 
                                                           
                                                             2 
                                                              
                                                             n 
                                                           
                                                         
                                                          
                                                         
                                                           sin 
                                                            
                                                           
                                                             ( 
                                                             
                                                             
                                                             γ 
                                                             n 
                                                             
                                                             + 
                                                             θ 
                                                             
                                                             ) 
                                                           
                                                         
                                                       
                                                     
                                                     } 
                                                   
                                                 
                                               
                                               〉 
                                             
                                           
                                           + 
                                           
                                             
                                               
                                                 z 
                                                 ¨ 
                                               
                                               
                                                 6 
                                                  
                                                 n 
                                               
                                             
                                              
                                             
                                               m 
                                               sn 
                                             
                                              
                                             
                                               { 
                                               
                                                 
                                                   
                                                     c 
                                                     
                                                       1 
                                                        
                                                       n 
                                                     
                                                   
                                                    
                                                   sin 
                                                    
                                                   
                                                       
                                                   
                                                    
                                                   
                                                     η 
                                                     n 
                                                   
                                                 
                                                 + 
                                                 
                                                   
                                                     b 
                                                     
                                                       2 
                                                        
                                                       n 
                                                     
                                                   
                                                    
                                                   
                                                     cos 
                                                      
                                                     
                                                       ( 
                                                       
                                                         
                                                           γ 
                                                           n 
                                                         
                                                         + 
                                                         
                                                           η 
                                                           n 
                                                         
                                                       
                                                       ) 
                                                     
                                                   
                                                 
                                               
                                               } 
                                             
                                           
                                           + 
                                           
                                             
                                               
                                                 z 
                                                 . 
                                               
                                               
                                                 6 
                                                  
                                                 n 
                                               
                                             
                                              
                                             
                                               
                                                 η 
                                                 . 
                                               
                                               n 
                                             
                                              
                                             
                                               m 
                                               sn 
                                             
                                              
                                             
                                               { 
                                               
                                                 
                                                   
                                                     c 
                                                     
                                                       1 
                                                        
                                                       n 
                                                     
                                                   
                                                    
                                                   cos 
                                                    
                                                   
                                                       
                                                   
                                                    
                                                   
                                                     η 
                                                     n 
                                                   
                                                 
                                                 - 
                                                 
                                                   
                                                     b 
                                                     
                                                       2 
                                                        
                                                       n 
                                                     
                                                   
                                                    
                                                   
                                                     sin 
                                                      
                                                     
                                                       ( 
                                                       
                                                         
                                                           γ 
                                                           n 
                                                         
                                                         + 
                                                         
                                                           η 
                                                           n 
                                                         
                                                       
                                                       ) 
                                                     
                                                   
                                                 
                                               
                                               } 
                                             
                                           
                                           + 
                                           
                                             
                                               
                                                 η 
                                                 ¨ 
                                               
                                               n 
                                             
                                              
                                             
                                               m 
                                               sn 
                                             
                                              
                                             
                                               z 
                                               
                                                 6 
                                                  
                                                 n 
                                               
                                             
                                              
                                             
                                               { 
                                               
                                                 
                                                   z 
                                                   
                                                     6 
                                                      
                                                     n 
                                                   
                                                 
                                                 + 
                                                 
                                                   
                                                     c 
                                                     
                                                       1 
                                                        
                                                       n 
                                                     
                                                   
                                                    
                                                   cos 
                                                    
                                                   
                                                       
                                                   
                                                    
                                                   
                                                     η 
                                                     n 
                                                   
                                                 
                                                 - 
                                                 
                                                   
                                                     b 
                                                     
                                                       2 
                                                        
                                                       n 
                                                     
                                                   
                                                    
                                                   
                                                     sin 
                                                      
                                                     
                                                       ( 
                                                       
                                                         
                                                           γ 
                                                           n 
                                                         
                                                         + 
                                                         
                                                           η 
                                                           n 
                                                         
                                                       
                                                       ) 
                                                     
                                                   
                                                 
                                               
                                               } 
                                             
                                           
                                           + 
                                           
                                             
                                               
                                                 η 
                                                 . 
                                               
                                               n 
                                             
                                              
                                             
                                               m 
                                               sn 
                                             
                                              
                                             
                                               
                                                 z 
                                                 . 
                                               
                                               
                                                 6 
                                                  
                                                 n 
                                               
                                             
                                              
                                             
                                               { 
                                               
                                                 
                                                   z 
                                                   
                                                     6 
                                                      
                                                     n 
                                                   
                                                 
                                                 + 
                                                 
                                                   
                                                     c 
                                                     
                                                       1 
                                                        
                                                       n 
                                                     
                                                   
                                                    
                                                   cos 
                                                    
                                                   
                                                       
                                                   
                                                    
                                                   
                                                     η 
                                                     n 
                                                   
                                                 
                                                 - 
                                                 
                                                   
                                                     b 
                                                     
                                                       2 
                                                        
                                                       n 
                                                     
                                                   
                                                    
                                                   
                                                     sin 
                                                      
                                                     
                                                       ( 
                                                       
                                                         
                                                           γ 
                                                           n 
                                                         
                                                         + 
                                                         
                                                           η 
                                                           n 
                                                         
                                                       
                                                       ) 
                                                     
                                                   
                                                 
                                               
                                               } 
                                             
                                           
                                           + 
                                           
                                             
                                               
                                                 η 
                                                 . 
                                               
                                               n 
                                             
                                              
                                             
                                               m 
                                               sn 
                                             
                                              
                                             
                                               z 
                                               
                                                 6 
                                                  
                                                 n 
                                               
                                             
                                              
                                             
                                               { 
                                               
                                                 
                                                   
                                                     z 
                                                     . 
                                                   
                                                   
                                                     6 
                                                      
                                                     n 
                                                   
                                                 
                                                 - 
                                                 
                                                   
                                                     
                                                       η 
                                                       . 
                                                     
                                                     n 
                                                   
                                                    
                                                   
                                                     [ 
                                                     
                                                       
                                                         
                                                           c 
                                                           
                                                             1 
                                                              
                                                             n 
                                                           
                                                         
                                                          
                                                         sin 
                                                          
                                                         
                                                             
                                                         
                                                          
                                                         
                                                           η 
                                                           n 
                                                         
                                                       
                                                       + 
                                                       
                                                         
                                                           b 
                                                           
                                                             2 
                                                              
                                                             n 
                                                           
                                                         
                                                          
                                                         
                                                           cos 
                                                            
                                                           
                                                             ( 
                                                             
                                                             
                                                             γ 
                                                             n 
                                                             
                                                             + 
                                                             
                                                             η 
                                                             n 
                                                             
                                                             
                                                             ) 
                                                           
                                                         
                                                       
                                                     
                                                     ] 
                                                   
                                                 
                                               
                                               } 
                                             
                                           
                                           + 
                                           
                                             
                                               θ 
                                               ¨ 
                                             
                                              
                                             
                                               [ 
                                               
                                                 
                                                   m 
                                                   aw2In 
                                                 
                                                 - 
                                                 
                                                   
                                                     m 
                                                     aw1n 
                                                   
                                                    
                                                   
                                                     { 
                                                     
                                                       
                                                         
                                                           c 
                                                           
                                                             2 
                                                              
                                                             n 
                                                           
                                                         
                                                          
                                                         sin 
                                                          
                                                         
                                                             
                                                         
                                                          
                                                         
                                                           θ 
                                                           n 
                                                         
                                                       
                                                       - 
                                                       
                                                         
                                                           b 
                                                           
                                                             2 
                                                              
                                                             n 
                                                           
                                                         
                                                          
                                                         
                                                           cos 
                                                            
                                                           
                                                             ( 
                                                             
                                                             
                                                             γ 
                                                             n 
                                                             
                                                             + 
                                                             
                                                             θ 
                                                             n 
                                                             
                                                             
                                                             ) 
                                                           
                                                         
                                                       
                                                     
                                                     } 
                                                   
                                                 
                                               
                                               ] 
                                             
                                           
                                           - 
                                           
                                             
                                               
                                                 θ 
                                                 . 
                                               
                                               n 
                                               2 
                                             
                                              
                                             
                                               m 
                                               aw1n 
                                             
                                              
                                             
                                               { 
                                               
                                                 
                                                   
                                                     c 
                                                     
                                                       2 
                                                        
                                                       n 
                                                     
                                                   
                                                    
                                                   cos 
                                                    
                                                   
                                                       
                                                   
                                                    
                                                   
                                                     θ 
                                                     n 
                                                   
                                                 
                                                 + 
                                                 
                                                   
                                                     b 
                                                     
                                                       2 
                                                        
                                                       n 
                                                     
                                                   
                                                    
                                                   
                                                     sin 
                                                      
                                                     
                                                       ( 
                                                       
                                                         
                                                           γ 
                                                           n 
                                                         
                                                         + 
                                                         
                                                           θ 
                                                           n 
                                                         
                                                       
                                                       ) 
                                                     
                                                   
                                                 
                                               
                                               } 
                                             
                                           
                                         
                                         ] 
                                       
                                       + 
                                       
                                         
                                           β 
                                           ¨ 
                                         
                                          
                                         
                                           a 
                                           
                                             1 
                                              
                                             n 
                                           
                                         
                                          
                                         
                                           { 
                                           
                                             
                                               
                                                 m 
                                                 sawcn 
                                               
                                                
                                               
                                                 sin 
                                                  
                                                 
                                                   ( 
                                                   
                                                     α 
                                                     + 
                                                     
                                                       γ 
                                                       n 
                                                     
                                                   
                                                   ) 
                                                 
                                               
                                             
                                             - 
                                             
                                               
                                                 m 
                                                 sawbn 
                                               
                                                
                                               cos 
                                                
                                               
                                                   
                                               
                                                
                                               α 
                                             
                                             + 
                                             
                                               
                                                 m 
                                                 sn 
                                               
                                                
                                               
                                                 z 
                                                 
                                                   6 
                                                    
                                                   n 
                                                 
                                               
                                                
                                               
                                                 sin 
                                                  
                                                 
                                                   ( 
                                                   
                                                     α 
                                                     + 
                                                     
                                                       γ 
                                                       n 
                                                     
                                                     + 
                                                     
                                                       η 
                                                       n 
                                                     
                                                   
                                                   ) 
                                                 
                                               
                                             
                                             - 
                                             
                                               
                                                 m 
                                                 aw1n 
                                               
                                                
                                               
                                                 cos 
                                                  
                                                 
                                                   ( 
                                                   
                                                     α 
                                                     + 
                                                     
                                                       γ 
                                                       n 
                                                     
                                                     + 
                                                     
                                                       θ 
                                                       n 
                                                     
                                                   
                                                   ) 
                                                 
                                               
                                             
                                           
                                           } 
                                         
                                       
                                       + 
                                       
                                         
                                           β 
                                           . 
                                         
                                          
                                         
                                           a 
                                           
                                             1 
                                              
                                             n 
                                           
                                         
                                          
                                         
                                           { 
                                           
                                             
                                               
                                                 α 
                                                 . 
                                               
                                                
                                               
                                                 [ 
                                                 
                                                   
                                                     
                                                       m 
                                                       sawcn 
                                                     
                                                      
                                                     
                                                       cos 
                                                        
                                                       
                                                         ( 
                                                         
                                                           α 
                                                           + 
                                                           
                                                             γ 
                                                             n 
                                                           
                                                         
                                                         ) 
                                                       
                                                     
                                                   
                                                   + 
                                                   
                                                     
                                                       m 
                                                       sawbn 
                                                     
                                                      
                                                     sin 
                                                      
                                                     
                                                         
                                                     
                                                      
                                                     α 
                                                   
                                                 
                                                 ] 
                                               
                                             
                                             + 
                                             
                                               
                                                 m 
                                                 sn 
                                               
                                                
                                               
                                                 
                                                   z 
                                                   . 
                                                 
                                                 
                                                   6 
                                                    
                                                   n 
                                                 
                                               
                                                
                                               
                                                 sin 
                                                  
                                                 
                                                   ( 
                                                   
                                                     α 
                                                     + 
                                                     
                                                       γ 
                                                       n 
                                                     
                                                     + 
                                                     
                                                       η 
                                                       n 
                                                     
                                                   
                                                   ) 
                                                 
                                               
                                             
                                             + 
                                             
                                               
                                                 ( 
                                                 
                                                   
                                                     α 
                                                     . 
                                                   
                                                   + 
                                                   
                                                     
                                                       η 
                                                       . 
                                                     
                                                     n 
                                                   
                                                 
                                                 ) 
                                               
                                                
                                               
                                                 m 
                                                 sn 
                                               
                                                
                                               
                                                 z 
                                                 
                                                   6 
                                                    
                                                   n 
                                                 
                                               
                                                
                                               
                                                 cos 
                                                  
                                                 
                                                   ( 
                                                   
                                                     α 
                                                     + 
                                                     
                                                       γ 
                                                       n 
                                                     
                                                     + 
                                                     
                                                       η 
                                                       n 
                                                     
                                                   
                                                   ) 
                                                 
                                               
                                             
                                             + 
                                             
                                               
                                                 ( 
                                                 
                                                   
                                                     α 
                                                     . 
                                                   
                                                   + 
                                                   
                                                     
                                                       θ 
                                                       . 
                                                     
                                                     n 
                                                   
                                                 
                                                 ) 
                                               
                                                
                                               
                                                 m 
                                                 aw1n 
                                               
                                                
                                               
                                                 sin 
                                                  
                                                 
                                                   ( 
                                                   
                                                     α 
                                                     + 
                                                     
                                                       γ 
                                                       n 
                                                     
                                                     + 
                                                     
                                                       θ 
                                                       n 
                                                     
                                                   
                                                   ) 
                                                 
                                               
                                             
                                           
                                           } 
                                         
                                       
                                       + 
                                       
                                         
                                           
                                             z 
                                             ¨ 
                                           
                                           0 
                                         
                                          
                                         
                                           { 
                                           
                                             
                                               
                                                 m 
                                                 aw1n 
                                               
                                                
                                               
                                                 cos 
                                                  
                                                 
                                                   ( 
                                                   
                                                     α 
                                                     + 
                                                     
                                                       γ 
                                                       n 
                                                     
                                                     + 
                                                     
                                                       θ 
                                                       n 
                                                     
                                                   
                                                   ) 
                                                 
                                               
                                             
                                             - 
                                             
                                               
                                                 z 
                                                 
                                                   6 
                                                    
                                                   n 
                                                 
                                               
                                                
                                               
                                                 m 
                                                 sn 
                                               
                                                
                                               
                                                 sin 
                                                  
                                                 
                                                   ( 
                                                   
                                                     α 
                                                     + 
                                                     
                                                       γ 
                                                       n 
                                                     
                                                     + 
                                                     
                                                       η 
                                                       n 
                                                     
                                                   
                                                   ) 
                                                 
                                               
                                             
                                             - 
                                             
                                               
                                                 m 
                                                 sawcn 
                                               
                                                
                                               
                                                 sin 
                                                  
                                                 
                                                   ( 
                                                   
                                                     α 
                                                     + 
                                                     
                                                       γ 
                                                       n 
                                                     
                                                   
                                                   ) 
                                                 
                                               
                                             
                                             + 
                                             
                                               
                                                 m 
                                                 sawbn 
                                               
                                                
                                               cos 
                                                
                                               
                                                   
                                               
                                                
                                               α 
                                             
                                           
                                           } 
                                         
                                          
                                         cos 
                                          
                                         
                                             
                                         
                                          
                                         β 
                                       
                                     
                                     } 
                                   
                                   + 
                                   
                                     
                                       
                                         z 
                                         . 
                                       
                                       0 
                                     
                                      
                                     
                                       { 
                                       
                                         
                                           
                                             - 
                                             
                                               ( 
                                               
                                                 
                                                   α 
                                                   . 
                                                 
                                                 + 
                                                 
                                                   
                                                     θ 
                                                     . 
                                                   
                                                   n 
                                                 
                                               
                                               ) 
                                             
                                           
                                            
                                           
                                             m 
                                             aw1n 
                                           
                                            
                                           
                                             sin 
                                              
                                             
                                               ( 
                                               
                                                 α 
                                                 + 
                                                 
                                                   γ 
                                                   n 
                                                 
                                                 + 
                                                 
                                                   θ 
                                                   n 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                         - 
                                         
                                           
                                             z 
                                             
                                               6 
                                                
                                               n 
                                             
                                           
                                            
                                           
                                             m 
                                             sn 
                                           
                                            
                                           
                                             sin 
                                              
                                             
                                               ( 
                                               
                                                 α 
                                                 + 
                                                 
                                                   γ 
                                                   n 
                                                 
                                                 + 
                                                 
                                                   η 
                                                   n 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                         - 
                                         
                                           
                                             ( 
                                             
                                               
                                                 α 
                                                 . 
                                               
                                               + 
                                               
                                                 
                                                   θ 
                                                   . 
                                                 
                                                 n 
                                               
                                             
                                             ) 
                                           
                                            
                                           
                                             z 
                                             
                                               6 
                                                
                                               n 
                                             
                                           
                                            
                                           
                                             m 
                                             sn 
                                           
                                            
                                           
                                             cos 
                                              
                                             
                                               ( 
                                               
                                                 α 
                                                 + 
                                                 
                                                   γ 
                                                   n 
                                                 
                                                 + 
                                                 
                                                   η 
                                                   n 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                         - 
                                         
                                           
                                             α 
                                             . 
                                           
                                            
                                           
                                             m 
                                             sawcn 
                                           
                                            
                                           
                                             cos 
                                              
                                             
                                               ( 
                                               
                                                 α 
                                                 + 
                                                 
                                                   γ 
                                                   n 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                         - 
                                         
                                           
                                             α 
                                             . 
                                           
                                            
                                           
                                             m 
                                             sawbn 
                                           
                                            
                                           sin 
                                            
                                           
                                               
                                           
                                            
                                           α 
                                         
                                       
                                       } 
                                     
                                      
                                     cos 
                                      
                                     
                                         
                                     
                                      
                                     β 
                                   
                                   - 
                                   
                                     
                                       β 
                                       . 
                                     
                                      
                                     
                                       
                                         z 
                                         . 
                                       
                                       0 
                                     
                                      
                                     
                                       { 
                                       
                                         
                                           
                                             m 
                                             aw1n 
                                           
                                            
                                           
                                             cos 
                                              
                                             
                                               ( 
                                               
                                                 α 
                                                 + 
                                                 
                                                   γ 
                                                   n 
                                                 
                                                 + 
                                                 
                                                   θ 
                                                   n 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                         - 
                                         
                                           
                                             z 
                                             
                                               6 
                                                
                                               n 
                                             
                                           
                                            
                                           
                                             m 
                                             sn 
                                           
                                            
                                           
                                             sin 
                                              
                                             
                                               ( 
                                               
                                                 α 
                                                 + 
                                                 
                                                   γ 
                                                   n 
                                                 
                                                 + 
                                                 
                                                   η 
                                                   n 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                         - 
                                         
                                           
                                             m 
                                             sawcn 
                                           
                                            
                                           
                                             sin 
                                              
                                             
                                               ( 
                                               
                                                 α 
                                                 + 
                                                 
                                                   γ 
                                                   n 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                         + 
                                         
                                           
                                             m 
                                             sawbn 
                                           
                                            
                                           cos 
                                            
                                           
                                               
                                           
                                            
                                           α 
                                         
                                       
                                       } 
                                     
                                      
                                     cos 
                                      
                                     
                                         
                                     
                                      
                                     β 
                                   
                                 
                                 } 
                               
                               - 
                               
                                 
                                   { 
                                   
                                     
                                       
                                         
                                           β 
                                           . 
                                         
                                         2 
                                       
                                        
                                       
                                         
                                           m 
                                           b 
                                         
                                          
                                         
                                           ( 
                                           
                                             
                                               
                                                 b 
                                                 0 
                                               
                                                
                                               cos 
                                                
                                               
                                                   
                                               
                                                
                                               α 
                                             
                                             - 
                                             
                                               
                                                 c 
                                                 0 
                                               
                                                
                                               sin 
                                                
                                               
                                                   
                                               
                                                
                                               α 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                     + 
                                     
                                       
                                         α 
                                         . 
                                       
                                        
                                       
                                         β 
                                         . 
                                       
                                        
                                       
                                         m 
                                         ba 
                                       
                                     
                                   
                                   } 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       
                                         b 
                                         0 
                                       
                                        
                                       sin 
                                        
                                       
                                           
                                       
                                        
                                       α 
                                     
                                     + 
                                     
                                       
                                         c 
                                         0 
                                       
                                        
                                       cos 
                                        
                                       
                                           
                                       
                                        
                                       α 
                                     
                                   
                                   ) 
                                 
                               
                               - 
                               
                                  
                                 
                                   
                                     
                                       
                                         β 
                                         . 
                                       
                                       2 
                                     
                                      
                                     
                                       〈 
                                       
                                         
                                           
                                             m 
                                             sn 
                                           
                                            
                                           
                                             { 
                                             
                                               
                                                 
                                                   z 
                                                   
                                                     
                                                       6 
                                                        
                                                       n 
                                                     
                                                      
                                                     
                                                         
                                                     
                                                   
                                                 
                                                  
                                                 
                                                   cos 
                                                    
                                                   
                                                     ( 
                                                     
                                                       α 
                                                       + 
                                                       
                                                         γ 
                                                         n 
                                                       
                                                       + 
                                                       
                                                         η 
                                                         n 
                                                       
                                                     
                                                     ) 
                                                   
                                                 
                                               
                                               + 
                                               
                                                 
                                                   c 
                                                   
                                                     1 
                                                      
                                                     n 
                                                   
                                                 
                                                  
                                                 
                                                   cos 
                                                    
                                                   
                                                     ( 
                                                     
                                                       α 
                                                       + 
                                                       
                                                         γ 
                                                         n 
                                                       
                                                     
                                                     ) 
                                                   
                                                 
                                               
                                               + 
                                               
                                                 
                                                   b 
                                                   
                                                     2 
                                                      
                                                     n 
                                                   
                                                 
                                                  
                                                 sin 
                                                  
                                                 
                                                     
                                                 
                                                  
                                                 α 
                                               
                                             
                                             } 
                                           
                                            
                                           
                                             { 
                                             
                                               
                                                 
                                                   - 
                                                   
                                                     z 
                                                     
                                                       6 
                                                        
                                                       n 
                                                     
                                                   
                                                 
                                                  
                                                 
                                                   sin 
                                                    
                                                   
                                                     ( 
                                                     
                                                       α 
                                                       + 
                                                       
                                                         γ 
                                                         n 
                                                       
                                                       + 
                                                       
                                                         η 
                                                         n 
                                                       
                                                     
                                                     ) 
                                                   
                                                 
                                               
                                               - 
                                               
                                                 
                                                   c 
                                                   
                                                     1 
                                                      
                                                     n 
                                                   
                                                 
                                                  
                                                 
                                                   sin 
                                                    
                                                   
                                                     ( 
                                                     
                                                       α 
                                                       + 
                                                       
                                                         γ 
                                                         n 
                                                       
                                                     
                                                     ) 
                                                   
                                                 
                                               
                                               + 
                                               
                                                 
                                                   b 
                                                   
                                                     2 
                                                      
                                                     n 
                                                   
                                                 
                                                  
                                                 cos 
                                                  
                                                 
                                                     
                                                 
                                                  
                                                 α 
                                               
                                             
                                             } 
                                           
                                         
                                         + 
                                         
                                           
                                             m 
                                             an 
                                           
                                            
                                           
                                             { 
                                             
                                               
                                                 
                                                   e 
                                                   
                                                     1 
                                                      
                                                     n 
                                                   
                                                 
                                                  
                                                 sin 
                                                  
                                                 
                                                     
                                                 
                                                  
                                                 
                                                   ( 
                                                   
                                                     α 
                                                     + 
                                                     
                                                       γ 
                                                       n 
                                                     
                                                     + 
                                                     
                                                       θ 
                                                       n 
                                                     
                                                   
                                                   ) 
                                                 
                                               
                                               + 
                                               
                                                 
                                                   c 
                                                   
                                                     2 
                                                      
                                                     n 
                                                   
                                                 
                                                  
                                                 
                                                   cos 
                                                    
                                                   
                                                     ( 
                                                     
                                                       α 
                                                       + 
                                                       
                                                         γ 
                                                         n 
                                                       
                                                     
                                                     ) 
                                                   
                                                 
                                               
                                               + 
                                               
                                                 
                                                   b 
                                                   
                                                     2 
                                                      
                                                     n 
                                                   
                                                 
                                                  
                                                 sin 
                                                  
                                                 
                                                     
                                                 
                                                  
                                                 α 
                                               
                                             
                                             } 
                                           
                                            
                                           
                                             { 
                                             
                                               
                                                 
                                                   e 
                                                   1 
                                                 
                                                  
                                                 
                                                   cos 
                                                    
                                                   
                                                     ( 
                                                     
                                                       α 
                                                       + 
                                                       
                                                         γ 
                                                         n 
                                                       
                                                       + 
                                                       
                                                         θ 
                                                         n 
                                                       
                                                     
                                                     ) 
                                                   
                                                 
                                               
                                               - 
                                               
                                                 
                                                   c 
                                                   
                                                     2 
                                                      
                                                     n 
                                                   
                                                 
                                                  
                                                 
                                                   sin 
                                                    
                                                   
                                                     ( 
                                                     
                                                       α 
                                                       + 
                                                       
                                                         γ 
                                                         n 
                                                       
                                                     
                                                     ) 
                                                   
                                                 
                                               
                                               + 
                                               
                                                 
                                                   b 
                                                   
                                                     2 
                                                      
                                                     n 
                                                   
                                                 
                                                  
                                                 cos 
                                                  
                                                 
                                                     
                                                 
                                                  
                                                 α 
                                               
                                             
                                             } 
                                           
                                         
                                         + 
                                         
                                           
                                             m 
                                             wn 
                                           
                                            
                                           
                                             { 
                                             
                                               
                                                 
                                                   e 
                                                   
                                                     3 
                                                      
                                                     n 
                                                   
                                                 
                                                  
                                                 
                                                   sin 
                                                    
                                                   
                                                     ( 
                                                     
                                                       α 
                                                       + 
                                                       
                                                         γ 
                                                         n 
                                                       
                                                       + 
                                                       
                                                         θ 
                                                         n 
                                                       
                                                     
                                                     ) 
                                                   
                                                 
                                               
                                               + 
                                               
                                                 
                                                   c 
                                                   
                                                     2 
                                                      
                                                     n 
                                                   
                                                 
                                                  
                                                 
                                                   cos 
                                                    
                                                   
                                                     ( 
                                                     
                                                       α 
                                                       + 
                                                       
                                                         γ 
                                                         n 
                                                       
                                                     
                                                     ) 
                                                   
                                                 
                                               
                                               + 
                                               
                                                 
                                                   b 
                                                   
                                                     2 
                                                      
                                                     n 
                                                   
                                                 
                                                  
                                                 sin 
                                                  
                                                 
                                                     
                                                 
                                                  
                                                 α 
                                               
                                             
                                             } 
                                           
                                            
                                           
                                             { 
                                             
                                               
                                                 
                                                   e 
                                                   3 
                                                 
                                                  
                                                 
                                                   cos 
                                                    
                                                   
                                                     ( 
                                                     
                                                       α 
                                                       + 
                                                       
                                                         γ 
                                                         n 
                                                       
                                                       + 
                                                       
                                                         θ 
                                                         n 
                                                       
                                                     
                                                     ) 
                                                   
                                                 
                                               
                                               - 
                                               
                                                 
                                                   c 
                                                   
                                                     2 
                                                      
                                                     n 
                                                   
                                                 
                                                  
                                                 
                                                   sin 
                                                    
                                                   
                                                     ( 
                                                     
                                                       α 
                                                       + 
                                                       
                                                         γ 
                                                         n 
                                                       
                                                     
                                                     ) 
                                                   
                                                 
                                               
                                               + 
                                               
                                                 
                                                   b 
                                                   
                                                     2 
                                                      
                                                     n 
                                                   
                                                 
                                                  
                                                 cos 
                                                  
                                                 
                                                     
                                                 
                                                  
                                                 α 
                                               
                                             
                                             } 
                                           
                                         
                                       
                                       〉 
                                     
                                   
                                   + 
                                   
                                     
                                       
                                         z 
                                         . 
                                       
                                       
                                         6 
                                          
                                         n 
                                       
                                     
                                      
                                     
                                       β 
                                       . 
                                     
                                      
                                     
                                       m 
                                       sn 
                                     
                                      
                                     
                                       a 
                                       
                                         1 
                                          
                                         n 
                                       
                                     
                                      
                                     
                                       sin 
                                        
                                       
                                         ( 
                                         
                                           α 
                                           + 
                                           
                                             γ 
                                             n 
                                           
                                           + 
                                           
                                             η 
                                             n 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                   + 
                                   
                                     
                                       
                                         η 
                                         . 
                                       
                                       n 
                                     
                                      
                                     
                                       β 
                                       . 
                                     
                                      
                                     
                                       m 
                                       sn 
                                     
                                      
                                     
                                       z 
                                       
                                         6 
                                          
                                         n 
                                       
                                     
                                      
                                     
                                       a 
                                       
                                         1 
                                          
                                         n 
                                       
                                     
                                      
                                     
                                       cos 
                                        
                                       
                                         ( 
                                         
                                           α 
                                           + 
                                           
                                             γ 
                                             n 
                                           
                                           + 
                                           
                                             η 
                                             n 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                   + 
                                   
                                     
                                       θ 
                                       . 
                                     
                                      
                                     
                                       β 
                                       . 
                                     
                                      
                                     
                                       m 
                                       aw1n 
                                     
                                      
                                     
                                       a 
                                       
                                         1 
                                          
                                         n 
                                       
                                     
                                      
                                     
                                       sin 
                                        
                                       
                                         ( 
                                         
                                           α 
                                           + 
                                           
                                             γ 
                                             n 
                                           
                                           + 
                                           
                                             θ 
                                             n 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                   + 
                                   
                                     
                                       α 
                                       . 
                                     
                                      
                                     
                                       β 
                                       . 
                                     
                                      
                                     
                                       a 
                                       
                                         1 
                                          
                                         n 
                                       
                                     
                                      
                                     
                                       { 
                                       
                                         
                                           
                                             m 
                                             sawcn 
                                           
                                            
                                           
                                             cos 
                                              
                                             
                                               ( 
                                               
                                                 α 
                                                 + 
                                                 
                                                   γ 
                                                   n 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                         + 
                                         
                                           
                                             m 
                                             sawbn 
                                           
                                            
                                           sin 
                                            
                                           
                                               
                                           
                                            
                                           α 
                                         
                                         + 
                                         
                                           
                                             m 
                                             sn 
                                           
                                            
                                           
                                             z 
                                             
                                               6 
                                                
                                               n 
                                             
                                           
                                            
                                           
                                             cos 
                                              
                                             
                                               ( 
                                               
                                                 α 
                                                 + 
                                                 
                                                   γ 
                                                   n 
                                                 
                                                 + 
                                                 
                                                   η 
                                                   n 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                         + 
                                         
                                           
                                             m 
                                             aw1n 
                                           
                                            
                                           
                                             sin 
                                              
                                             
                                               ( 
                                               
                                                 α 
                                                 + 
                                                 
                                                   γ 
                                                   n 
                                                 
                                                 + 
                                                 
                                                   θ 
                                                   n 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                       
                                       } 
                                     
                                   
                                   - 
                                   
                                     
                                       
                                         z 
                                         . 
                                       
                                       0 
                                     
                                      
                                     
                                       { 
                                       
                                         
                                           
                                             
                                               z 
                                               . 
                                             
                                             
                                               6 
                                                
                                               n 
                                             
                                           
                                            
                                           
                                             m 
                                             sn 
                                           
                                            
                                           
                                             sin 
                                              
                                             
                                               ( 
                                               
                                                 α 
                                                 + 
                                                 
                                                   γ 
                                                   n 
                                                 
                                                 + 
                                                 
                                                   η 
                                                   n 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                         + 
                                         
                                           
                                             ( 
                                             
                                               
                                                 α 
                                                 . 
                                               
                                               + 
                                               
                                                 
                                                   θ 
                                                   . 
                                                 
                                                 n 
                                               
                                             
                                             ) 
                                           
                                            
                                           
                                             m 
                                             aw1n 
                                           
                                            
                                           
                                             sin 
                                              
                                             
                                               ( 
                                               
                                                 α 
                                                 + 
                                                 
                                                   γ 
                                                   n 
                                                 
                                                 + 
                                                 
                                                   θ 
                                                   n 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                         + 
                                         
                                           
                                             ( 
                                             
                                               
                                                 α 
                                                 . 
                                               
                                               + 
                                               
                                                 
                                                   η 
                                                   . 
                                                 
                                                 n 
                                               
                                             
                                             ) 
                                           
                                            
                                           
                                             z 
                                             
                                               6 
                                                
                                               n 
                                             
                                           
                                            
                                           
                                             m 
                                             sn 
                                           
                                            
                                           
                                             cos 
                                              
                                             
                                               ( 
                                               
                                                 α 
                                                 + 
                                                 
                                                   γ 
                                                   n 
                                                 
                                                 + 
                                                 
                                                   θ 
                                                   n 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                         + 
                                         
                                           
                                             α 
                                             . 
                                           
                                            
                                           
                                             m 
                                             sawcn 
                                           
                                            
                                           
                                             cos 
                                              
                                             
                                               ( 
                                               
                                                 α 
                                                 + 
                                                 
                                                   γ 
                                                   n 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                         + 
                                         
                                            
                                           
                                             
                                               α 
                                               . 
                                             
                                              
                                             
                                               m 
                                               sawbn 
                                             
                                              
                                             sin 
                                              
                                             
                                                 
                                             
                                              
                                             α 
                                           
                                         
                                       
                                     
                                   
                                 
                               
                             
                             } 
                           
                            
                           
                              
                             
                               cos 
                                
                               
                                   
                               
                                
                               β 
                                
                               
                                 β 
                                 . 
                               
                                
                               
                                 
                                   z 
                                   . 
                                 
                                 0 
                               
                               [ 
                               
                                 
                                   { 
                                   
                                     
                                       
                                         m 
                                         aw1n 
                                       
                                        
                                       
                                         cos 
                                          
                                         
                                           ( 
                                           
                                             α 
                                             + 
                                             
                                               γ 
                                               n 
                                             
                                             + 
                                             
                                               θ 
                                               n 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                     - 
                                     
                                       
                                         z 
                                         
                                           6 
                                            
                                           n 
                                         
                                       
                                        
                                       
                                         m 
                                         sn 
                                       
                                        
                                       
                                         sin 
                                          
                                         
                                           ( 
                                           
                                             α 
                                             + 
                                             
                                               γ 
                                               n 
                                             
                                             + 
                                             
                                               η 
                                               n 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                     - 
                                     
                                       
                                         m 
                                         sawn 
                                       
                                        
                                       
                                         sin 
                                          
                                         
                                           ( 
                                           
                                             α 
                                             + 
                                             
                                               γ 
                                               n 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                     + 
                                     
                                       
                                         m 
                                         sawbn 
                                       
                                        
                                       cos 
                                        
                                       
                                           
                                       
                                        
                                       α 
                                     
                                   
                                   } 
                                 
                                  
                                 sin 
                                  
                                 
                                     
                                 
                                  
                                 β 
                                  
                               
                             
                           
                         
                          
                       
                       + 
                       
                         
                           
                             gm 
                             b 
                           
                            
                           
                             ( 
                             
                               
                                 
                                   b 
                                   0 
                                 
                                  
                                 cos 
                                  
                                 
                                     
                                 
                                  
                                 α 
                               
                               - 
                               
                                 
                                   c 
                                   0 
                                 
                                  
                                 sin 
                                  
                                 
                                     
                                 
                                  
                                 α 
                               
                             
                             ) 
                           
                         
                          
                         
                            
                           
                             
                               cos 
                                
                               
                                   
                               
                                
                               β 
                             
                             - 
                             
                                
                               
                                  
                                 
                                    
                                   
                                      
                                     
                                        
                                       
                                         g 
                                          
                                         
                                            
                                           
                                             
                                               { 
                                               
                                                 
                                                   
                                                     m 
                                                     sn 
                                                   
                                                    
                                                   
                                                     z 
                                                     
                                                       6 
                                                        
                                                       n 
                                                     
                                                   
                                                    
                                                   
                                                     sin 
                                                      
                                                     
                                                       ( 
                                                       
                                                         α 
                                                         + 
                                                         
                                                           γ 
                                                           n 
                                                         
                                                         + 
                                                         
                                                           η 
                                                           n 
                                                         
                                                       
                                                       ) 
                                                     
                                                   
                                                 
                                                 - 
                                                 
                                                   
                                                     m 
                                                     aw1n 
                                                   
                                                    
                                                   
                                                     cos 
                                                      
                                                     
                                                       ( 
                                                       
                                                         α 
                                                         + 
                                                         
                                                           γ 
                                                           n 
                                                         
                                                         + 
                                                         
                                                           θ 
                                                           n 
                                                         
                                                       
                                                       ) 
                                                     
                                                   
                                                 
                                                 + 
                                                 
                                                   
                                                     m 
                                                     sawcn 
                                                   
                                                    
                                                   
                                                     sin 
                                                      
                                                     
                                                       ( 
                                                       
                                                         α 
                                                         + 
                                                         
                                                           γ 
                                                           n 
                                                         
                                                       
                                                       ) 
                                                     
                                                   
                                                 
                                                 - 
                                                 
                                                   
                                                     m 
                                                     sawbn 
                                                   
                                                    
                                                   cos 
                                                    
                                                   
                                                       
                                                   
                                                    
                                                   α 
                                                 
                                               
                                               } 
                                             
                                              
                                             
                                                
                                               
                                                  
                                                 
                                                   
                                                     cos 
                                                      
                                                     
                                                         
                                                     
                                                      
                                                     β 
                                                   
                                                   = 
                                                   
                                                      
                                                     
                                                       
                                                         λ 
                                                         
                                                           3 
                                                            
                                                           n 
                                                         
                                                       
                                                        
                                                       
                                                         { 
                                                         
                                                           
                                                             
                                                             - 
                                                             
                                                             z 
                                                             
                                                             12 
                                                              
                                                             n 
                                                             
                                                             
                                                             
                                                              
                                                             sin 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             α 
                                                           
                                                           + 
                                                           
                                                             
                                                             e 
                                                             
                                                             3 
                                                              
                                                             n 
                                                             
                                                             
                                                              
                                                             
                                                             cos 
                                                              
                                                             
                                                             ( 
                                                             
                                                             α 
                                                             + 
                                                             
                                                             γ 
                                                             n 
                                                             
                                                             + 
                                                             
                                                             θ 
                                                             n 
                                                             
                                                             
                                                             ) 
                                                             
                                                             
                                                           
                                                           - 
                                                           
                                                              
                                                             
                                                             
                                                             
                                                             c 
                                                             
                                                             2 
                                                              
                                                             n 
                                                             
                                                             
                                                              
                                                             
                                                             sin 
                                                              
                                                             
                                                             ( 
                                                             
                                                             α 
                                                             + 
                                                             
                                                             γ 
                                                             n 
                                                             
                                                             
                                                             ) 
                                                             
                                                             
                                                             
                                                             + 
                                                             
                                                             
                                                             b 
                                                             
                                                             2 
                                                              
                                                             n 
                                                             
                                                             
                                                              
                                                             cos 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             α 
                                                             
                                                             
                                                           
                                                         
                                                       
                                                     
                                                   
                                                 
                                               
                                             
                                           
                                         
                                       
                                     
                                   
                                 
                               
                             
                           
                         
                       
                     
                     } 
                   
                    
                   cos 
                    
                   
                       
                   
                    
                   β 
                    
                 
               
               
                 
                   ( 
                   5.94 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           z 
                           ¨ 
                         
                         0 
                       
                        
                       
                         { 
                         
                           
                             
                               m 
                               b 
                             
                              
                             
                               A 
                               2 
                             
                           
                           + 
                           
                             
                               m 
                               aw1n 
                             
                              
                             
                               C 
                               
                                 αγθ 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                           
                           - 
                           
                             
                               z 
                               
                                 6 
                                  
                                 n 
                               
                             
                              
                             
                               m 
                               sn 
                             
                              
                             
                               S 
                               
                                 αγη 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                           
                           - 
                           
                             
                               m 
                               sawcn 
                             
                              
                             
                               S 
                               
                                 αγ 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                           
                           + 
                           
                             
                               m 
                               sawbn 
                             
                              
                             
                               C 
                               α 
                             
                           
                         
                         } 
                       
                        
                       
                         C 
                         β 
                       
                     
                     - 
                     
                       
                         β 
                         ¨ 
                       
                        
                       
                         m 
                         ba 
                       
                        
                       
                         A 
                         2 
                       
                     
                     + 
                     
                       
                         α 
                         ¨ 
                       
                        
                       
                         { 
                         
                           
                             m 
                             bbI 
                           
                           + 
                           
                             m 
                             sawIn 
                           
                           + 
                           
                             
                               m 
                               sn 
                             
                              
                             
                               
                                 z 
                                 
                                   6 
                                    
                                   n 
                                 
                               
                                
                               
                                 ( 
                                 
                                   
                                     z 
                                     
                                       6 
                                        
                                       n 
                                     
                                   
                                   + 
                                   
                                     2 
                                      
                                     
                                       E 
                                       
                                         1 
                                          
                                         n 
                                       
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                           - 
                           
                             2 
                              
                             
                               m 
                               aw1n 
                             
                              
                             
                               H 
                               
                                 1 
                                  
                                 n 
                               
                             
                           
                         
                         } 
                       
                     
                     + 
                     
                       2 
                        
                       
                           
                       
                        
                       
                         α 
                         . 
                       
                        
                       
                         { 
                         
                           
                             
                               m 
                               sn 
                             
                              
                             
                               
                                 
                                   z 
                                   . 
                                 
                                 
                                   6 
                                    
                                   n 
                                 
                               
                                
                               
                                 ( 
                                 
                                   
                                     z 
                                     
                                       6 
                                        
                                       n 
                                     
                                   
                                   + 
                                   
                                     E 
                                     
                                       1 
                                        
                                       n 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                           - 
                           
                             
                               m 
                               sn 
                             
                              
                             
                               z 
                               
                                 6 
                                  
                                 n 
                               
                             
                              
                             
                               
                                 η 
                                 . 
                               
                               n 
                             
                              
                             
                               E 
                               
                                 2 
                                  
                                 n 
                               
                             
                           
                           - 
                           
                             
                               
                                 θ 
                                 . 
                               
                               n 
                             
                              
                             
                               m 
                               aw1n 
                             
                              
                             
                               H 
                               
                                 2 
                                  
                                 n 
                               
                             
                           
                         
                         } 
                       
                     
                     + 
                     
                       
                         
                           z 
                           ¨ 
                         
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         E 
                         
                           2 
                            
                           n 
                         
                       
                     
                     + 
                     
                       
                         
                           z 
                           . 
                         
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         
                           η 
                           . 
                         
                         n 
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         E 
                         
                           1 
                            
                           n 
                         
                       
                     
                     + 
                     
                       
                         
                           η 
                           ¨ 
                         
                         n 
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         z 
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         { 
                         
                           
                             z 
                             
                               6 
                                
                               n 
                             
                           
                           + 
                           
                             E 
                             
                               1 
                                
                               n 
                             
                           
                         
                         } 
                       
                     
                     + 
                     
                       
                         
                           η 
                           . 
                         
                         n 
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         
                           z 
                           . 
                         
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         { 
                         
                           
                             2 
                              
                             
                               z 
                               
                                 6 
                                  
                                 n 
                               
                             
                           
                           + 
                           
                             E 
                             
                               1 
                                
                               n 
                             
                           
                         
                         } 
                       
                     
                     - 
                     
                       
                         
                           η 
                           . 
                         
                         n 
                         2 
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         z 
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         E 
                         
                           2 
                            
                           n 
                         
                       
                     
                     + 
                     
                       
                         θ 
                         ¨ 
                       
                        
                       
                         ( 
                         
                           
                             m 
                             aw2In 
                           
                           - 
                           
                             
                               m 
                               aw1n 
                             
                              
                             
                               H 
                               
                                 1 
                                  
                                 n 
                               
                             
                           
                         
                         ) 
                       
                     
                     - 
                     
                       
                         
                           θ 
                           . 
                         
                         n 
                         2 
                       
                        
                       
                         m 
                         aw1n 
                       
                        
                       
                         H 
                         
                           2 
                            
                           n 
                         
                       
                     
                     + 
                     
                       
                         β 
                         ¨ 
                       
                        
                       
                         
                           a 
                           
                             1 
                              
                             n 
                           
                         
                          
                         
                           ( 
                           
                             
                               
                                 m 
                                 sawcn 
                               
                                
                               
                                 S 
                                 
                                   αγ 
                                    
                                   
                                       
                                   
                                    
                                   n 
                                 
                               
                             
                             - 
                             
                               
                                 m 
                                 sawbn 
                               
                                
                               
                                 C 
                                 α 
                               
                             
                             + 
                             
                               
                                 m 
                                 sn 
                               
                                
                               
                                 z 
                                 
                                   6 
                                    
                                   n 
                                 
                               
                                
                               
                                 S 
                                 
                                   αγη 
                                    
                                   
                                       
                                   
                                    
                                   n 
                                 
                               
                             
                             - 
                             
                               
                                 m 
                                 aw1n 
                               
                                
                               
                                 C 
                                 
                                   αγθ 
                                    
                                   
                                       
                                   
                                    
                                   n 
                                 
                               
                             
                           
                           ) 
                         
                       
                     
                     + 
                     
                       
                         β 
                         . 
                       
                        
                       
                         a 
                         
                           1 
                            
                           n 
                         
                       
                        
                       
                         { 
                         
                           
                             
                               α 
                               . 
                             
                              
                             
                               ( 
                               
                                 
                                   
                                     m 
                                     sawcn 
                                   
                                    
                                   
                                     C 
                                     
                                       αγ 
                                        
                                       
                                           
                                       
                                        
                                       n 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     m 
                                     sawbn 
                                   
                                    
                                   
                                     S 
                                     α 
                                   
                                 
                               
                               ) 
                             
                           
                           + 
                           
                             
                               m 
                               sn 
                             
                              
                             
                               
                                 z 
                                 . 
                               
                               
                                 6 
                                  
                                 n 
                               
                             
                              
                             
                               S 
                               
                                 αγη 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                           
                           + 
                           
                             
                               ( 
                               
                                 
                                   α 
                                   . 
                                 
                                 + 
                                 
                                   
                                     η 
                                     . 
                                   
                                   n 
                                 
                               
                               ) 
                             
                              
                             
                               m 
                               sn 
                             
                              
                             
                               z 
                               
                                 6 
                                  
                                 n 
                               
                             
                              
                             
                               C 
                               
                                 αγη 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                           
                           + 
                           
                             
                               ( 
                               
                                 
                                   α 
                                   . 
                                 
                                 + 
                                 
                                   
                                     θ 
                                     . 
                                   
                                   n 
                                 
                               
                               ) 
                             
                              
                             
                               m 
                               aw1n 
                             
                              
                             
                               S 
                               
                                 αγθ 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                           
                         
                         } 
                       
                     
                     - 
                     
                       
                         
                           β 
                           . 
                         
                         2 
                       
                        
                       
                         m 
                         b 
                       
                        
                       
                         A 
                         2 
                       
                        
                       
                         A 
                         1 
                       
                     
                     - 
                     
                       [ 
                       
                         
                           
                             
                               β 
                               . 
                             
                             2 
                           
                            
                           
                             { 
                             
                               
                                 
                                   m 
                                   sn 
                                 
                                  
                                 
                                   
                                     B 
                                     1 
                                   
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           - 
                                           
                                             z 
                                             
                                               6 
                                                
                                               n 
                                             
                                           
                                         
                                          
                                         
                                           S 
                                           
                                             αγη 
                                              
                                             
                                                 
                                             
                                              
                                             n 
                                           
                                         
                                       
                                       - 
                                       
                                         A 
                                         4 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               + 
                               
                                 
                                   m 
                                   an 
                                 
                                  
                                 
                                   
                                     B 
                                     2 
                                   
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           e 
                                           1 
                                         
                                          
                                         
                                           C 
                                           
                                             αγθ 
                                              
                                             
                                                 
                                             
                                              
                                             n 
                                           
                                         
                                       
                                       - 
                                       
                                         A 
                                         6 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               + 
                               
                                 
                                   m 
                                   wn 
                                 
                                  
                                 
                                   
                                     B 
                                     3 
                                   
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           e 
                                           3 
                                         
                                          
                                         
                                           C 
                                           
                                             αγθ 
                                              
                                             
                                                 
                                             
                                              
                                             n 
                                           
                                         
                                       
                                       - 
                                       
                                         A 
                                         6 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                             } 
                           
                         
                         + 
                         
                           
                             
                               z 
                               . 
                             
                             
                               6 
                                
                               n 
                             
                           
                            
                           
                             β 
                             . 
                           
                            
                           
                             m 
                             sn 
                           
                            
                           
                             a 
                             
                               1 
                                
                               n 
                             
                           
                            
                           
                             S 
                             
                               αγη 
                                
                               
                                   
                               
                                
                               n 
                             
                           
                         
                         + 
                         
                           
                             
                               η 
                               . 
                             
                             n 
                           
                            
                           
                             β 
                             . 
                           
                            
                           
                             m 
                             sn 
                           
                            
                           
                             z 
                             
                               6 
                                
                               n 
                             
                           
                            
                           
                             a 
                             
                               1 
                                
                               n 
                             
                           
                            
                           
                             C 
                             
                               αγη 
                                
                               
                                   
                               
                                
                               n 
                             
                           
                         
                         + 
                         
                           
                             θ 
                             . 
                           
                            
                           
                             β 
                             . 
                           
                            
                           
                             m 
                             aw1n 
                           
                            
                           
                             a 
                             
                               1 
                                
                               n 
                             
                           
                            
                           
                             S 
                             
                               αγθ 
                                
                               
                                   
                               
                                
                               n 
                             
                           
                         
                         + 
                         
                           
                             α 
                             . 
                           
                            
                           
                             β 
                             . 
                           
                            
                           
                             a 
                             
                               1 
                                
                               n 
                             
                           
                            
                           
                             { 
                             
                               
                                 
                                   m 
                                   sawcn 
                                 
                                  
                                 
                                   C 
                                   
                                     αγ 
                                      
                                     
                                         
                                     
                                      
                                     n 
                                   
                                 
                               
                               + 
                               
                                 
                                   m 
                                   sawbn 
                                 
                                  
                                 
                                   S 
                                   α 
                                 
                               
                               + 
                               
                                 
                                   m 
                                   sn 
                                 
                                  
                                 
                                   z 
                                   
                                     6 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   C 
                                   
                                     αγη 
                                      
                                     
                                         
                                     
                                      
                                     n 
                                   
                                 
                               
                               + 
                               
                                 
                                   m 
                                   aw1n 
                                 
                                  
                                 
                                   S 
                                   
                                     αγθ 
                                      
                                     
                                         
                                     
                                      
                                     n 
                                   
                                 
                               
                             
                             } 
                           
                         
                       
                       ] 
                     
                     + 
                     
                       
                         gm 
                         b 
                       
                        
                       
                         A 
                         2 
                       
                        
                       
                         C 
                         β 
                       
                     
                     - 
                     
                       g 
                        
                       
                         { 
                         
                           
                             
                               m 
                               sn 
                             
                              
                             
                               z 
                               
                                 6 
                                  
                                 n 
                               
                             
                              
                             
                               S 
                               
                                 αγη 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                           
                           - 
                           
                             
                               m 
                               aw1n 
                             
                              
                             
                               C 
                               
                                 αγθ 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                           
                           + 
                           
                             
                               m 
                               sawcn 
                             
                              
                             
                               S 
                               
                                 αγ 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                           
                           - 
                           
                             
                               m 
                               sawbn 
                             
                              
                             
                               C 
                               α 
                             
                           
                         
                         } 
                       
                        
                       
                         C 
                         β 
                       
                     
                   
                   = 
                   
                     
                       λ 
                       
                         3 
                          
                         n 
                       
                     
                      
                     
                       { 
                       
                         
                           
                             - 
                             
                               z 
                               
                                 12 
                                  
                                 n 
                               
                             
                           
                            
                           
                             S 
                             α 
                           
                         
                         + 
                         
                           
                             e 
                             
                               3 
                                
                               n 
                             
                           
                            
                           
                             C 
                             
                               αγθ 
                                
                               
                                   
                               
                                
                               n 
                             
                           
                         
                         - 
                         
                           
                             c 
                             
                               2 
                                
                               n 
                             
                           
                            
                           
                             S 
                             
                               αγ 
                                
                               
                                   
                               
                                
                               n 
                             
                           
                         
                         + 
                         
                           
                             b 
                             
                               2 
                                
                               n 
                             
                           
                            
                           
                             C 
                             α 
                           
                         
                       
                       } 
                     
                      
                     
                       C 
                       β 
                     
                   
                 
               
               
                 
                   ( 
                   5.95 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           z 
                           ¨ 
                         
                         0 
                       
                        
                       
                         { 
                         
                           
                             
                               m 
                               b 
                             
                              
                             
                               A 
                               2 
                             
                           
                           + 
                           
                             
                               m 
                               aw1n 
                             
                              
                             
                               C 
                               
                                 αγθ 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                           
                           - 
                           
                             
                               z 
                               
                                 6 
                                  
                                 n 
                               
                             
                              
                             
                               m 
                               sn 
                             
                              
                             
                               S 
                               
                                 αγη 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                           
                           - 
                           
                             
                               m 
                               sawcn 
                             
                              
                             
                               S 
                               
                                 αγ 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                           
                           + 
                           
                             
                               m 
                               sawbn 
                             
                              
                             
                               C 
                               α 
                             
                           
                         
                         } 
                       
                        
                       
                         C 
                         β 
                       
                     
                     - 
                     
                       
                         β 
                         ¨ 
                       
                        
                       
                         m 
                         ba 
                       
                        
                       
                         A 
                         2 
                       
                     
                     + 
                     
                       
                         α 
                         ¨ 
                       
                        
                       
                         { 
                         
                           
                             m 
                             bbI 
                           
                           + 
                           
                             m 
                             sawIn 
                           
                           + 
                           
                             
                               m 
                               sn 
                             
                              
                             
                               
                                 z 
                                 
                                   6 
                                    
                                   n 
                                 
                               
                                
                               
                                 ( 
                                 
                                   
                                     z 
                                     
                                       6 
                                        
                                       n 
                                     
                                   
                                   + 
                                   
                                     2 
                                      
                                     
                                       E 
                                       
                                         1 
                                          
                                         n 
                                       
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                           - 
                           
                             2 
                              
                             
                               m 
                               aw1n 
                             
                              
                             
                               H 
                               
                                 1 
                                  
                                 n 
                               
                             
                           
                         
                         } 
                       
                     
                     + 
                     
                       
                         
                           m 
                           sn 
                         
                          
                         
                           ( 
                           
                             
                               2 
                                
                               
                                   
                               
                                
                               
                                 α 
                                 . 
                               
                                
                               
                                 
                                   z 
                                   . 
                                 
                                 
                                   6 
                                    
                                   n 
                                 
                               
                             
                             + 
                             
                               
                                 
                                   η 
                                   ¨ 
                                 
                                 n 
                               
                                
                               
                                 z 
                                 
                                   6 
                                    
                                   n 
                                 
                               
                             
                             + 
                             
                               2 
                                
                               
                                 
                                   η 
                                   . 
                                 
                                 n 
                               
                                
                               
                                 
                                   z 
                                   . 
                                 
                                 
                                   6 
                                    
                                   n 
                                 
                               
                             
                           
                           ) 
                         
                       
                        
                       
                         ( 
                         
                           
                             z 
                             
                               6 
                                
                               n 
                             
                           
                           + 
                           
                             E 
                             
                               1 
                                
                               n 
                             
                           
                         
                         ) 
                       
                     
                     - 
                     
                       2 
                        
                       
                           
                       
                        
                       
                         
                           α 
                           . 
                         
                          
                         
                           ( 
                           
                             
                               
                                 m 
                                 sn 
                               
                                
                               
                                 z 
                                 
                                   6 
                                    
                                   n 
                                 
                               
                                
                               
                                 
                                   η 
                                   . 
                                 
                                 n 
                               
                                
                               
                                 E 
                                 
                                   2 
                                    
                                   n 
                                 
                               
                             
                             + 
                             
                               
                                 
                                   θ 
                                   . 
                                 
                                 n 
                               
                                
                               
                                 m 
                                 aw1n 
                               
                                
                               
                                 H 
                                 
                                   2 
                                    
                                   n 
                                 
                               
                             
                           
                           ) 
                         
                       
                     
                     + 
                     
                       
                         
                           z 
                           ¨ 
                         
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         E 
                         
                           2 
                            
                           n 
                         
                       
                     
                     - 
                     
                       
                         
                           η 
                           . 
                         
                         n 
                         2 
                       
                        
                       
                         m 
                         
                           sn 
                            
                           
                               
                           
                         
                       
                        
                       
                         z 
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         E 
                         
                           2 
                            
                           n 
                         
                       
                     
                     + 
                     
                       
                         θ 
                         ¨ 
                       
                        
                       
                         ( 
                         
                           
                             m 
                             aw2In 
                           
                           - 
                           
                             
                               m 
                               aw1n 
                             
                              
                             
                               H 
                               
                                 1 
                                  
                                 n 
                               
                             
                           
                         
                         ) 
                       
                     
                     - 
                     
                       
                         
                           θ 
                           . 
                         
                         n 
                         2 
                       
                        
                       
                         m 
                         aw1n 
                       
                        
                       
                         H 
                         
                           2 
                            
                           n 
                         
                       
                     
                     + 
                     
                       
                         β 
                         ¨ 
                       
                        
                       
                         
                           a 
                           
                             1 
                              
                             n 
                           
                         
                          
                         
                           ( 
                           
                             
                               
                                 m 
                                 sawcn 
                               
                                
                               
                                 S 
                                 
                                   αγ 
                                    
                                   
                                       
                                   
                                    
                                   n 
                                 
                               
                             
                             - 
                             
                               
                                 m 
                                 sawbn 
                               
                                
                               
                                 C 
                                 α 
                               
                             
                             + 
                             
                               
                                 m 
                                 sn 
                               
                                
                               
                                 z 
                                 
                                   6 
                                    
                                   n 
                                 
                               
                                
                               
                                 S 
                                 
                                   αγη 
                                    
                                   
                                       
                                   
                                    
                                   n 
                                 
                               
                             
                             - 
                             
                               
                                 m 
                                 aw1n 
                               
                                
                               
                                 C 
                                 
                                   αγθ 
                                    
                                   
                                       
                                   
                                    
                                   n 
                                 
                               
                             
                           
                           ) 
                         
                       
                     
                     - 
                     
                       
                         
                           
                             β 
                             . 
                           
                            
                           
                               
                           
                         
                         2 
                       
                        
                       
                         { 
                         
                           
                             
                               m 
                               b 
                             
                              
                             
                               A 
                               2 
                             
                              
                             
                               A 
                               1 
                             
                           
                           + 
                           
                             
                               m 
                               sn 
                             
                              
                             
                               
                                 B 
                                 1 
                               
                                
                               
                                 ( 
                                 
                                   
                                     
                                       - 
                                       
                                         z 
                                         
                                           6 
                                            
                                           n 
                                         
                                       
                                     
                                      
                                     
                                       S 
                                       
                                         αγη 
                                          
                                         
                                             
                                         
                                          
                                         n 
                                       
                                     
                                   
                                   - 
                                   
                                     A 
                                     4 
                                   
                                 
                                 ) 
                               
                             
                           
                           + 
                           
                             
                               m 
                               an 
                             
                              
                             
                               
                                 B 
                                 2 
                               
                                
                               
                                 ( 
                                 
                                   
                                     
                                       e 
                                       1 
                                     
                                      
                                     
                                       C 
                                       
                                         αγθ 
                                          
                                         
                                             
                                         
                                          
                                         n 
                                       
                                     
                                   
                                   - 
                                   
                                     A 
                                     6 
                                   
                                 
                                 ) 
                               
                             
                           
                           + 
                           
                             
                               m 
                               wn 
                             
                              
                             
                               
                                 B 
                                 3 
                               
                                
                               
                                 ( 
                                 
                                   
                                     
                                       e 
                                       3 
                                     
                                      
                                     
                                       C 
                                       
                                         αγθ 
                                          
                                         
                                             
                                         
                                          
                                         n 
                                       
                                     
                                   
                                   - 
                                   
                                     A 
                                     6 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         } 
                       
                     
                     + 
                     
                       
                         gm 
                         b 
                       
                        
                       
                         A 
                         2 
                       
                        
                       
                         C 
                         β 
                       
                     
                     - 
                     
                       g 
                        
                       
                         { 
                         
                           
                             
                               m 
                               sn 
                             
                              
                             
                               z 
                               
                                 6 
                                  
                                 n 
                               
                             
                              
                             
                               S 
                               
                                 αγη 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                           
                           - 
                           
                             
                               m 
                               aw1n 
                             
                              
                             
                               C 
                               
                                 αγθ 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                           
                           + 
                           
                             
                               m 
                               sawcn 
                             
                              
                             
                               S 
                               
                                 αγ 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                           
                           - 
                           
                             
                               m 
                               sawbn 
                             
                              
                             
                               C 
                               α 
                             
                           
                         
                         } 
                       
                        
                       
                         C 
                         β 
                       
                     
                   
                   = 
                   
                     
                       
                         λ 
                         
                           3 
                            
                           n 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               - 
                               
                                 z 
                                 
                                   12 
                                    
                                   n 
                                 
                               
                             
                              
                             
                               S 
                               α 
                             
                           
                           + 
                           
                             
                               e 
                               
                                 3 
                                  
                                 n 
                               
                             
                              
                             
                               C 
                               
                                 αγθ 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                           
                           - 
                           
                             
                               c 
                               
                                 2 
                                  
                                 n 
                               
                             
                              
                             
                               S 
                               
                                 αγ 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                           
                           + 
                           
                             
                               b 
                               
                                 2 
                                  
                                 n 
                               
                             
                              
                             
                               C 
                               α 
                             
                           
                         
                         ) 
                       
                     
                      
                     
                       C 
                       β 
                     
                   
                 
               
               
                 
                   ( 
                   5.96 
                   ) 
                 
               
             
             
               
                 ∴ 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     α 
                     ¨ 
                   
                   = 
                   
                     
                       
                           
                       
                        
                       
                         
                           
                             
                               z 
                               ¨ 
                             
                             0 
                           
                            
                           
                             { 
                             
                               
                                 
                                   m 
                                   b 
                                 
                                  
                                 
                                   A 
                                   2 
                                 
                               
                               + 
                               
                                 
                                   m 
                                   aw1n 
                                 
                                  
                                 
                                   C 
                                   
                                     αγθ 
                                      
                                     
                                         
                                     
                                      
                                     n 
                                   
                                 
                               
                               - 
                               
                                 
                                   z 
                                   
                                     6 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   m 
                                   sn 
                                 
                                  
                                 
                                   S 
                                   
                                     αγη 
                                      
                                     
                                         
                                     
                                      
                                     n 
                                   
                                 
                               
                               - 
                               
                                 
                                   m 
                                   sawcn 
                                 
                                  
                                 
                                   S 
                                   
                                     αγ 
                                      
                                     
                                         
                                     
                                      
                                     n 
                                   
                                 
                               
                               + 
                               
                                 
                                   m 
                                   sawbn 
                                 
                                  
                                 
                                   C 
                                   α 
                                 
                               
                             
                             } 
                           
                            
                           
                             C 
                             β 
                           
                         
                          
                         
                           
 
                         
                          
                         
                           
                             
                               
                                 m 
                                 sn 
                               
                                
                               
                                 ( 
                                 
                                   
                                     2 
                                      
                                     
                                       α 
                                       . 
                                     
                                      
                                     
                                       
                                         z 
                                         . 
                                       
                                       
                                         6 
                                          
                                         n 
                                       
                                     
                                   
                                   + 
                                   
                                     
                                       
                                         η 
                                         ¨ 
                                       
                                       n 
                                     
                                      
                                     
                                       z 
                                       
                                         6 
                                          
                                         n 
                                       
                                     
                                   
                                   + 
                                   
                                     2 
                                      
                                     
                                       
                                         η 
                                         . 
                                       
                                       n 
                                     
                                      
                                     
                                       
                                         z 
                                         . 
                                       
                                       
                                         6 
                                          
                                         n 
                                       
                                     
                                   
                                 
                                 ) 
                               
                             
                              
                             
                               ( 
                               
                                 
                                   z 
                                   
                                     6 
                                      
                                     n 
                                   
                                 
                                 + 
                                 
                                   E 
                                   
                                     1 
                                      
                                     n 
                                   
                                 
                               
                               ) 
                             
                           
                           - 
                           
                             2 
                              
                             
                               
                                 α 
                                 . 
                               
                                
                               
                                 ( 
                                 
                                   
                                     
                                       m 
                                       sn 
                                     
                                      
                                     
                                       z 
                                       
                                         6 
                                          
                                         n 
                                       
                                     
                                      
                                     
                                       
                                         η 
                                         . 
                                       
                                       n 
                                     
                                      
                                     
                                       E 
                                       
                                         2 
                                          
                                         n 
                                       
                                     
                                   
                                   + 
                                   
                                     
                                       
                                         θ 
                                         . 
                                       
                                       n 
                                     
                                      
                                     
                                       m 
                                       aw1n 
                                     
                                      
                                     
                                       H 
                                       
                                         2 
                                          
                                         n 
                                       
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                           + 
                           
                             
 
                           
                            
                           
                               
                           
                            
                           
                             
                               
                                 z 
                                 ¨ 
                               
                               
                                 6 
                                  
                                 n 
                               
                             
                              
                             
                               m 
                               sn 
                             
                              
                             
                               E 
                               
                                 2 
                                  
                                 n 
                               
                             
                           
                           - 
                           
                             
                               
                                 η 
                                 . 
                               
                               n 
                               2 
                             
                              
                             
                               m 
                               sn 
                             
                              
                             
                               z 
                               
                                 6 
                                  
                                 n 
                               
                             
                              
                             
                               E 
                               
                                 2 
                                  
                                 n 
                               
                             
                           
                           + 
                           
                             
                               θ 
                               ¨ 
                             
                              
                             
                               ( 
                               
                                 
                                   m 
                                   aw2In 
                                 
                                 - 
                                 
                                   
                                     m 
                                     aw1n 
                                   
                                    
                                   
                                     H 
                                     
                                       1 
                                        
                                       n 
                                     
                                   
                                 
                               
                               ) 
                             
                           
                           - 
                           
                             
                               
                                 θ 
                                 . 
                               
                               n 
                               2 
                             
                              
                             
                               m 
                               aw1n 
                             
                              
                             
                               H 
                               
                                 2 
                                  
                                 n 
                               
                             
                           
                           + 
                           
                             
 
                           
                            
                           
                               
                           
                            
                           
                             
                               β 
                               ¨ 
                             
                              
                             
                               
                                 a 
                                 
                                   1 
                                    
                                   n 
                                 
                               
                                
                               
                                 ( 
                                 
                                   
                                     
                                       m 
                                       sawcn 
                                     
                                      
                                     
                                       S 
                                       
                                         αγ 
                                          
                                         
                                             
                                         
                                          
                                         n 
                                       
                                     
                                   
                                   - 
                                   
                                     
                                       m 
                                       sawbn 
                                     
                                      
                                     
                                       C 
                                       α 
                                     
                                   
                                   + 
                                   
                                     
                                       m 
                                       sn 
                                     
                                      
                                     
                                       z 
                                       
                                         6 
                                          
                                         n 
                                       
                                     
                                      
                                     
                                       S 
                                       
                                         αγη 
                                          
                                         
                                             
                                         
                                          
                                         n 
                                       
                                     
                                   
                                   - 
                                   
                                     
                                       m 
                                       aw1n 
                                     
                                      
                                     
                                       C 
                                       
                                         αγθ 
                                          
                                         
                                             
                                         
                                          
                                         n 
                                       
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                           - 
                           
                             
 
                           
                            
                           
                               
                           
                            
                           
                             
                               
                                 β 
                                 . 
                               
                               2 
                             
                              
                             
                               { 
                               
                                 
                                   
                                     m 
                                     b 
                                   
                                    
                                   
                                     A 
                                     2 
                                   
                                    
                                   
                                     A 
                                     1 
                                   
                                 
                                 + 
                                 
                                   
                                     m 
                                     sn 
                                   
                                    
                                   
                                     
                                       B 
                                       1 
                                     
                                      
                                     
                                       ( 
                                       
                                         
                                           
                                             - 
                                             
                                               z 
                                               
                                                 6 
                                                  
                                                 n 
                                               
                                             
                                           
                                            
                                           
                                             S 
                                             
                                               αγη 
                                                
                                               
                                                   
                                               
                                                
                                               n 
                                             
                                           
                                         
                                         - 
                                         
                                           A 
                                           4 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     m 
                                     an 
                                   
                                    
                                   
                                     
                                       B 
                                       2 
                                     
                                      
                                     
                                       ( 
                                       
                                         
                                           
                                             e 
                                             1 
                                           
                                            
                                           
                                             C 
                                             
                                               αγθ 
                                                
                                               
                                                   
                                               
                                                
                                               n 
                                             
                                           
                                         
                                         - 
                                         
                                           A 
                                           6 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                 + 
                                 
                                   
 
                                 
                                  
                                 
                                     
                                 
                                  
                                 
                                   
                                     m 
                                     wn 
                                   
                                    
                                   
                                     
                                       B 
                                       3 
                                     
                                      
                                     
                                       ( 
                                       
                                         
                                           
                                             e 
                                             3 
                                           
                                            
                                           
                                             C 
                                             
                                               αγθ 
                                                
                                               
                                                   
                                               
                                                
                                               n 
                                             
                                           
                                         
                                         - 
                                         
                                           A 
                                           6 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                               
                               } 
                             
                           
                           + 
                           
                             
                               gm 
                               b 
                             
                              
                             
                               A 
                               2 
                             
                              
                             
                               C 
                               β 
                             
                           
                           - 
                           
                             g 
                              
                             
                               { 
                               
                                 
                                   
                                     m 
                                     
                                       sn 
                                        
                                       
                                           
                                       
                                     
                                   
                                    
                                   
                                     z 
                                     
                                       6 
                                        
                                       n 
                                     
                                   
                                    
                                   
                                     S 
                                     
                                       αγη 
                                        
                                       
                                           
                                       
                                        
                                       n 
                                     
                                   
                                 
                                 - 
                                 
                                   
                                     m 
                                     aw1n 
                                   
                                    
                                   
                                     C 
                                     
                                       αγθ 
                                        
                                       
                                           
                                       
                                        
                                       n 
                                     
                                   
                                 
                                 + 
                                 
                                   
 
                                 
                                  
                                 
                                     
                                 
                                  
                                 
                                   
                                     m 
                                     sawcn 
                                   
                                    
                                   
                                     S 
                                     
                                       αγ 
                                        
                                       
                                           
                                       
                                        
                                       n 
                                     
                                   
                                 
                                 - 
                                 
                                   
                                     m 
                                     sawbn 
                                   
                                    
                                   
                                     C 
                                     α 
                                   
                                 
                               
                               } 
                             
                              
                             
                               C 
                               β 
                             
                           
                           - 
                           
                             
                               β 
                               ¨ 
                             
                              
                             
                               m 
                               ba 
                             
                              
                             
                               A 
                               2 
                             
                           
                           + 
                           
                             
                               
                                 λ 
                                 
                                   3 
                                    
                                   n 
                                 
                               
                                
                               
                                 ( 
                                 
                                   
                                     
                                       z 
                                       
                                         12 
                                          
                                         n 
                                       
                                     
                                      
                                     
                                       S 
                                       α 
                                     
                                   
                                   - 
                                   
                                     
                                       e 
                                       
                                         3 
                                          
                                         n 
                                       
                                     
                                      
                                     
                                       C 
                                       
                                         αγθ 
                                          
                                         
                                             
                                         
                                          
                                         n 
                                       
                                     
                                   
                                   + 
                                   
                                     
 
                                   
                                    
                                   
                                       
                                   
                                    
                                   
                                     
                                       c 
                                       
                                         
                                           2 
                                            
                                           n 
                                         
                                          
                                         
                                             
                                         
                                       
                                     
                                      
                                     
                                       S 
                                       
                                         αγ 
                                          
                                         
                                             
                                         
                                          
                                         n 
                                       
                                     
                                   
                                   - 
                                   
                                     
                                       b 
                                       
                                         2 
                                          
                                         n 
                                       
                                     
                                      
                                     
                                       C 
                                       α 
                                     
                                   
                                 
                                 ) 
                               
                             
                              
                             
                               C 
                               β 
                             
                           
                         
                       
                     
                     
                       - 
                       
                         { 
                         
                           
                             m 
                             bbI 
                           
                           + 
                           
                             m 
                             sawIn 
                           
                           + 
                           
                             
                               m 
                               sn 
                             
                              
                             
                               
                                 z 
                                 
                                   6 
                                    
                                   n 
                                 
                               
                                
                               
                                 ( 
                                 
                                   
                                     z 
                                     
                                       6 
                                        
                                       n 
                                     
                                   
                                   + 
                                   
                                     2 
                                      
                                     
                                       E 
                                       
                                         1 
                                          
                                         n 
                                       
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                           - 
                           
                             2 
                              
                             
                               m 
                               aw1n 
                             
                              
                             
                               H 
                               
                                 1 
                                  
                                 n 
                               
                             
                           
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5.97 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                            
                           
                              
                             t 
                           
                         
                          
                         
                           ( 
                           
                             
                               ∂ 
                               L 
                             
                             
                               ∂ 
                               
                                 
                                   η 
                                   . 
                                 
                                 n 
                               
                             
                           
                           ) 
                         
                       
                       - 
                       
                         
                           ∂ 
                           L 
                         
                         
                           ∂ 
                           
                             η 
                             n 
                           
                         
                       
                     
                     = 
                     
                       
                         
                           
                             ∂ 
                             F 
                           
                           
                             ∂ 
                             
                               
                                 η 
                                 . 
                               
                               n 
                             
                           
                         
                         + 
                         
                           
                             ∑ 
                             
                               l 
                               , 
                               n 
                             
                           
                            
                           
                             
                               λ 
                               
                                 l 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                              
                             
                               a 
                               
                                 l 
                                  
                                 
                                     
                                 
                                  
                                 n 
                                  
                                 
                                     
                                 
                                  
                                 3 
                               
                             
                              
                             
                                 
                             
                              
                             l 
                           
                         
                       
                       = 
                       1 
                     
                   
                   , 
                   2 
                   , 
                   
                     
                       3 
                        
                       
                           
                       
                        
                       n 
                     
                     = 
                     i 
                   
                   , 
                   ii 
                   , 
                   iii 
                   , 
                   iv 
                 
               
               
                 
                   ( 
                   5.98 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         m 
                         sn 
                       
                        
                       
                         
                           η 
                           ¨ 
                         
                         n 
                       
                        
                       
                         z 
                         
                           6 
                            
                           n 
                         
                         2 
                       
                     
                     + 
                     
                       2 
                        
                       
                         m 
                         sn 
                       
                        
                       
                         
                           η 
                           . 
                         
                         n 
                       
                        
                       
                         
                           z 
                           . 
                         
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         z 
                         
                           6 
                            
                           n 
                         
                       
                     
                     + 
                     
                       
                         α 
                         ¨ 
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         z 
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         { 
                         
                           
                             z 
                             
                               6 
                                
                               n 
                             
                           
                           + 
                           
                             
                               c 
                               
                                 1 
                                  
                                 n 
                               
                             
                              
                             cos 
                              
                             
                                 
                             
                              
                             
                               η 
                               n 
                             
                           
                           - 
                           
                             
                               b 
                               
                                 2 
                                  
                                 n 
                               
                             
                              
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   
                                     γ 
                                     n 
                                   
                                   + 
                                   
                                     η 
                                     n 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         } 
                       
                     
                     + 
                     
                       
                         α 
                         . 
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         
                           z 
                           . 
                         
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         { 
                         
                           
                             z 
                             
                               6 
                                
                               n 
                             
                           
                           + 
                           
                             
                               c 
                               
                                 1 
                                  
                                 n 
                               
                             
                              
                             cos 
                              
                             
                                 
                             
                              
                             
                               η 
                               n 
                             
                           
                           - 
                           
                             
                               b 
                               
                                 2 
                                  
                                 n 
                               
                             
                              
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   
                                     γ 
                                     n 
                                   
                                   + 
                                   
                                     η 
                                     n 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         } 
                       
                     
                     + 
                     
                       
                         α 
                         . 
                       
                        
                       
                           
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         z 
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         { 
                         
                           
                             
                               z 
                               . 
                             
                             
                               6 
                                
                               n 
                             
                           
                           - 
                           
                             
                               
                                 η 
                                 . 
                               
                               n 
                             
                              
                             
                               [ 
                               
                                 
                                   
                                     c 
                                     
                                       1 
                                        
                                       n 
                                     
                                   
                                    
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   
                                     η 
                                     n 
                                   
                                 
                                 + 
                                 
                                   
                                     b 
                                     
                                       2 
                                        
                                       n 
                                     
                                   
                                    
                                   
                                     cos 
                                      
                                     
                                       ( 
                                       
                                         
                                           γ 
                                           n 
                                         
                                         + 
                                         
                                           η 
                                           n 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                               
                               ] 
                             
                           
                         
                         } 
                       
                     
                     + 
                     
                       
                         β 
                         ¨ 
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         z 
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         a 
                         
                           1 
                            
                           n 
                         
                       
                        
                       
                         sin 
                          
                         
                           ( 
                           
                             α 
                             + 
                             
                               γ 
                               n 
                             
                             + 
                             
                               η 
                               n 
                             
                           
                           ) 
                         
                       
                     
                     + 
                     
                       
                         β 
                         . 
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         
                           z 
                           . 
                         
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         a 
                         
                           1 
                            
                           n 
                         
                       
                        
                       
                         sin 
                          
                         
                           ( 
                           
                             α 
                             + 
                             
                               γ 
                               n 
                             
                             + 
                             
                               η 
                               n 
                             
                           
                           ) 
                         
                       
                     
                     + 
                     
                       
                         
                           β 
                           . 
                         
                          
                         
                           ( 
                           
                             
                               α 
                               . 
                             
                             + 
                             
                               
                                 η 
                                 . 
                               
                               n 
                             
                           
                           ) 
                         
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         z 
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         a 
                         
                           1 
                            
                           n 
                         
                       
                        
                       
                         cos 
                          
                         
                           ( 
                           
                             α 
                             + 
                             
                               γ 
                               n 
                             
                             + 
                             
                               η 
                               n 
                             
                           
                           ) 
                         
                       
                     
                     - 
                     
                       
                         
                           z 
                           ¨ 
                         
                         0 
                       
                        
                       
                         z 
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         sin 
                          
                         
                           ( 
                           
                             α 
                             + 
                             
                               γ 
                               n 
                             
                             + 
                             
                               η 
                               n 
                             
                           
                           ) 
                         
                       
                        
                       cos 
                        
                       
                           
                       
                        
                       β 
                     
                     - 
                     
                       
                         
                           z 
                           . 
                         
                         0 
                       
                        
                       
                         
                           z 
                           . 
                         
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         sin 
                          
                         
                           ( 
                           
                             α 
                             + 
                             
                               γ 
                               n 
                             
                             + 
                             
                               η 
                               n 
                             
                           
                           ) 
                         
                       
                        
                       cos 
                        
                       
                           
                       
                        
                       β 
                     
                     - 
                     
                       
                         ( 
                         
                           
                             α 
                             . 
                           
                           + 
                           
                             
                               η 
                               . 
                             
                             n 
                           
                         
                         ) 
                       
                        
                       
                         
                           z 
                           . 
                         
                         0 
                       
                        
                       
                         z 
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         cos 
                          
                         
                           ( 
                           
                             α 
                             + 
                             
                               γ 
                               n 
                             
                             + 
                             
                               η 
                               n 
                             
                           
                           ) 
                         
                       
                        
                       cos 
                        
                       
                           
                       
                        
                       β 
                     
                     - 
                     
                       
                         β 
                         . 
                       
                        
                       
                         
                           z 
                           . 
                         
                         0 
                       
                        
                       
                         
                           z 
                           . 
                         
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         sin 
                          
                         
                           ( 
                           
                             α 
                             + 
                             
                               γ 
                               n 
                             
                             + 
                             
                               η 
                               n 
                             
                           
                           ) 
                         
                       
                        
                       sin 
                        
                       
                           
                       
                        
                       β 
                     
                     - 
                     
                       〈 
                       
                         
                           
                             
                               α 
                               . 
                             
                             2 
                           
                            
                           
                             m 
                             sn 
                           
                            
                           
                             z 
                             
                               6 
                                
                               n 
                             
                           
                            
                           
                             { 
                             
                               
                                 
                                   - 
                                   
                                     c 
                                     
                                       1 
                                        
                                       n 
                                     
                                   
                                 
                                  
                                 sin 
                                  
                                 
                                     
                                 
                                  
                                 
                                   η 
                                   n 
                                 
                               
                               - 
                               
                                 
                                   b 
                                   
                                     2 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   cos 
                                    
                                   
                                     ( 
                                     
                                       
                                         γ 
                                         n 
                                       
                                       + 
                                       
                                         η 
                                         n 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                             } 
                           
                         
                         + 
                         
                           
                             
                               β 
                               . 
                             
                             2 
                           
                            
                           
                             m 
                             sn 
                           
                            
                           
                             { 
                             
                               
                                 
                                   z 
                                   
                                     6 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   cos 
                                    
                                   
                                     ( 
                                     
                                       α 
                                       + 
                                       
                                         γ 
                                         n 
                                       
                                       + 
                                       
                                         η 
                                         n 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               + 
                               
                                 
                                   c 
                                   
                                     1 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   cos 
                                    
                                   
                                     ( 
                                     
                                       α 
                                       + 
                                       
                                         γ 
                                         n 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               + 
                               
                                 
                                   b 
                                   
                                     2 
                                      
                                     n 
                                   
                                 
                                  
                                 sin 
                                  
                                 
                                     
                                 
                                  
                                 α 
                               
                             
                             } 
                           
                            
                           
                             { 
                             
                               
                                 - 
                                 
                                   z 
                                   
                                     6 
                                      
                                     n 
                                   
                                 
                               
                                
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     α 
                                     + 
                                     
                                       γ 
                                       n 
                                     
                                     + 
                                     
                                       η 
                                       n 
                                     
                                   
                                   ) 
                                 
                               
                             
                             } 
                           
                         
                         + 
                         
                           
                             
                               z 
                               . 
                             
                             
                               6 
                                
                               n 
                             
                           
                            
                           
                             α 
                             . 
                           
                            
                           
                             m 
                             sn 
                           
                            
                           
                             { 
                             
                               
                                 
                                   c 
                                   
                                     1 
                                      
                                     n 
                                   
                                 
                                  
                                 cos 
                                  
                                 
                                     
                                 
                                  
                                 
                                   η 
                                   n 
                                 
                               
                               - 
                               
                                 
                                   b 
                                   
                                     2 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         γ 
                                         n 
                                       
                                       + 
                                       
                                         η 
                                         n 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                             } 
                           
                         
                         + 
                         
                           
                             
                               z 
                               . 
                             
                             
                               6 
                                
                               n 
                             
                           
                            
                           
                             β 
                             . 
                           
                            
                           
                             m 
                             sn 
                           
                            
                           
                             a 
                             
                               1 
                                
                               n 
                             
                           
                            
                           
                             sin 
                              
                             
                               ( 
                               
                                 α 
                                 + 
                                 
                                   γ 
                                   n 
                                 
                                 + 
                                 
                                   η 
                                   n 
                                 
                               
                               ) 
                             
                           
                         
                         - 
                         
                           
                             
                               η 
                               . 
                             
                             n 
                           
                            
                           
                             α 
                             . 
                           
                            
                           
                             m 
                             sn 
                           
                            
                           
                             z 
                             
                               6 
                                
                               n 
                             
                           
                            
                           
                             { 
                             
                               
                                 
                                   c 
                                   
                                     1 
                                      
                                     n 
                                   
                                 
                                  
                                 sin 
                                  
                                 
                                     
                                 
                                  
                                 
                                   η 
                                   n 
                                 
                               
                               + 
                               
                                 
                                   b 
                                   
                                     2 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   cos 
                                    
                                   
                                     ( 
                                     
                                       
                                         γ 
                                         n 
                                       
                                       + 
                                       
                                         η 
                                         n 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                             } 
                           
                         
                         + 
                         
                           
                             
                               η 
                               . 
                             
                             n 
                           
                            
                           
                             β 
                             . 
                           
                            
                           
                             m 
                             sn 
                           
                            
                           
                             z 
                             
                               6 
                                
                               n 
                             
                           
                            
                           
                             a 
                             
                               1 
                                
                               n 
                             
                           
                            
                           
                             cos 
                              
                             
                               ( 
                               
                                 α 
                                 + 
                                 
                                   γ 
                                   n 
                                 
                                 + 
                                 
                                   η 
                                   n 
                                 
                               
                               ) 
                             
                           
                         
                         + 
                         
                           
                             α 
                             . 
                           
                            
                           
                             β 
                             . 
                           
                            
                           
                             a 
                             
                               1 
                                
                               n 
                             
                           
                            
                           
                             m 
                             sn 
                           
                            
                           
                             z 
                             
                               6 
                                
                               n 
                             
                           
                            
                           
                             cos 
                              
                             
                               ( 
                               
                                 α 
                                 + 
                                 
                                   γ 
                                   n 
                                 
                                 + 
                                 
                                   η 
                                   n 
                                 
                               
                               ) 
                             
                           
                         
                         + 
                         
                           
                             gm 
                             sn 
                           
                            
                           
                             z 
                             
                               6 
                                
                               n 
                             
                           
                            
                           
                             sin 
                              
                             
                               ( 
                               
                                 α 
                                 + 
                                 
                                   γ 
                                   n 
                                 
                                 + 
                                 
                                   η 
                                   n 
                                 
                               
                               ) 
                             
                           
                            
                           cos 
                            
                           
                               
                           
                            
                           β 
                         
                         - 
                         
                           
                             
                               z 
                               . 
                             
                             0 
                           
                            
                           
                             { 
                             
                               
                                 
                                   z 
                                   
                                     6 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   m 
                                   sn 
                                 
                                  
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       α 
                                       + 
                                       
                                         γ 
                                         n 
                                       
                                       + 
                                       
                                         η 
                                         n 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               + 
                               
                                 
                                   ( 
                                   
                                     
                                       α 
                                       . 
                                     
                                     + 
                                     
                                       
                                         η 
                                         . 
                                       
                                       n 
                                     
                                   
                                   ) 
                                 
                                  
                                 
                                   
                                     z 
                                     . 
                                   
                                   0 
                                 
                                  
                                 
                                   z 
                                   
                                     6 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   m 
                                   sn 
                                 
                                  
                                 
                                   cos 
                                    
                                   
                                     ( 
                                     
                                       α 
                                       + 
                                       
                                         γ 
                                         n 
                                       
                                       + 
                                       
                                         η 
                                         n 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                             } 
                           
                            
                           cos 
                            
                           
                               
                           
                            
                           β 
                         
                         + 
                         
                           
                             β 
                             . 
                           
                            
                           
                             
                               z 
                               . 
                             
                             0 
                           
                            
                           
                             
                               z 
                               . 
                             
                             
                               6 
                                
                               n 
                             
                           
                            
                           
                             m 
                             sn 
                           
                            
                           
                             sin 
                              
                             
                               ( 
                               
                                 α 
                                 + 
                                 
                                   γ 
                                   n 
                                 
                                 + 
                                 
                                   η 
                                   n 
                                 
                               
                               ) 
                             
                           
                            
                           sin 
                            
                           
                               
                           
                            
                           β 
                         
                       
                       〉 
                     
                   
                   = 
                   
                     
                       
                         - 
                         
                           
                             λ 
                             
                               1 
                                
                               n 
                             
                           
                            
                           
                             ( 
                             
                               
                                 z 
                                 
                                   6 
                                    
                                   n 
                                 
                               
                               - 
                               
                                 d 
                                 
                                   1 
                                    
                                   n 
                                 
                               
                             
                             ) 
                           
                         
                       
                        
                       cos 
                        
                       
                           
                       
                        
                       
                         η 
                         n 
                       
                     
                     + 
                     
                       
                         
                           λ 
                           
                             2 
                              
                             n 
                           
                         
                          
                         
                           ( 
                           
                             
                               z 
                               
                                 6 
                                  
                                 n 
                               
                             
                             - 
                             
                               d 
                               
                                 1 
                                  
                                 n 
                               
                             
                           
                           ) 
                         
                       
                        
                       sin 
                        
                       
                           
                       
                        
                       
                         η 
                         n 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5.99 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         m 
                         sn 
                       
                        
                       
                         
                           η 
                           ¨ 
                         
                         n 
                       
                        
                       
                         z 
                         
                           6 
                            
                           n 
                         
                         2 
                       
                     
                     + 
                     
                       2 
                        
                       
                         m 
                         sn 
                       
                        
                       
                         
                           η 
                           . 
                         
                         n 
                       
                        
                       
                         
                           z 
                           . 
                         
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         z 
                         
                           6 
                            
                           n 
                         
                       
                     
                     + 
                     
                       
                         α 
                         ¨ 
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         z 
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         { 
                         
                           
                             z 
                             
                               6 
                                
                               n 
                             
                           
                           + 
                           
                             E 
                             1 
                           
                         
                         } 
                       
                     
                     + 
                     
                       
                         α 
                         . 
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         
                           z 
                           . 
                         
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         { 
                         
                           
                             2 
                              
                             
                               z 
                               
                                 6 
                                  
                                 n 
                               
                             
                           
                           + 
                           
                             E 
                             1 
                           
                         
                         } 
                       
                     
                     - 
                     
                       
                         α 
                         . 
                       
                        
                       
                         m 
                         
                           sn 
                            
                           
                               
                           
                         
                       
                        
                       
                         z 
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         
                           η 
                           . 
                         
                         n 
                       
                        
                       
                         E 
                         2 
                       
                     
                     + 
                     
                       
                         β 
                         ¨ 
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         z 
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         a 
                         
                           1 
                            
                           n 
                         
                       
                        
                       
                         S 
                         
                           αγη 
                            
                           
                               
                           
                            
                           n 
                         
                       
                     
                     + 
                     
                       
                         β 
                         . 
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         
                           z 
                           . 
                         
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         a 
                         
                           1 
                            
                           n 
                         
                       
                        
                       
                         S 
                         
                           αγη 
                            
                           
                               
                           
                            
                           n 
                         
                       
                     
                     + 
                     
                       
                         
                           β 
                           . 
                         
                          
                         
                           ( 
                           
                             
                               α 
                               . 
                             
                             + 
                             
                               
                                 η 
                                 . 
                               
                               n 
                             
                           
                           ) 
                         
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         z 
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         a 
                         
                           1 
                            
                           n 
                         
                       
                        
                       
                         C 
                         
                           αγη 
                            
                           
                               
                           
                            
                           n 
                         
                       
                     
                     - 
                     
                       
                         
                           z 
                           ¨ 
                         
                         0 
                       
                        
                       
                         z 
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         S 
                         
                           αγη 
                            
                           
                               
                           
                            
                           n 
                         
                       
                        
                       
                         C 
                         β 
                       
                     
                     + 
                     
                       
                         
                           α 
                           . 
                         
                         2 
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         z 
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         E 
                         2 
                       
                     
                     + 
                     
                       
                         
                           β 
                           . 
                         
                         2 
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         B 
                         1 
                       
                        
                       
                         z 
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         S 
                         
                           αγη 
                            
                           
                               
                           
                            
                           n 
                         
                       
                     
                     - 
                     
                       
                         
                           z 
                           . 
                         
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         α 
                         . 
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         E 
                         1 
                       
                     
                     - 
                     
                       
                         
                           z 
                           . 
                         
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         β 
                         . 
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         a 
                         
                           1 
                            
                           n 
                         
                       
                        
                       
                         S 
                         
                           αγη 
                            
                           
                               
                           
                            
                           n 
                         
                       
                     
                     + 
                     
                       
                         
                           η 
                           . 
                         
                         n 
                       
                        
                       
                         α 
                         . 
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         z 
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         E 
                         2 
                       
                     
                     - 
                     
                       
                         
                           η 
                           . 
                         
                         n 
                       
                        
                       
                         β 
                         . 
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         z 
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         a 
                         
                           1 
                            
                           n 
                         
                       
                        
                       
                         C 
                         
                           αγη 
                            
                           
                               
                           
                            
                           n 
                         
                       
                     
                     - 
                     
                       
                         α 
                         . 
                       
                        
                       
                         β 
                         . 
                       
                        
                       
                         a 
                         
                           1 
                            
                           n 
                         
                       
                        
                       
                         m 
                         sn 
                       
                        
                       
                         z 
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         C 
                         
                           αγη 
                            
                           
                               
                           
                            
                           n 
                         
                       
                     
                     - 
                     
                       
                         gm 
                         sn 
                       
                        
                       
                         z 
                         
                           6 
                            
                           n 
                         
                       
                        
                       
                         S 
                         
                           αγη 
                            
                           
                               
                           
                            
                           n 
                         
                       
                        
                       
                         C 
                         β 
                       
                     
                   
                   = 
                   
                     
                       
                         - 
                         
                           
                             λ 
                             
                               1 
                                
                               n 
                             
                           
                            
                           
                             ( 
                             
                               
                                 z 
                                 
                                   6 
                                    
                                   n 
                                 
                               
                               - 
                               
                                 d 
                                 
                                   1 
                                    
                                   n 
                                 
                               
                             
                             ) 
                           
                         
                       
                        
                       
                         C 
                         
                           η 
                            
                           
                               
                           
                            
                           n 
                         
                       
                     
                     + 
                     
                       
                         
                           λ 
                           
                             2 
                              
                             n 
                           
                         
                          
                         
                           ( 
                           
                             
                               z 
                               
                                 6 
                                  
                                 n 
                               
                             
                             - 
                             
                               d 
                               
                                 1 
                                  
                                 n 
                               
                             
                           
                           ) 
                         
                       
                        
                       
                         S 
                         
                           η 
                            
                           
                               
                           
                            
                           n 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5.100 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       m 
                       sn 
                     
                      
                     
                       z 
                       
                         6 
                          
                         n 
                       
                     
                      
                     
                       { 
                       
                         
                           
                             
                               η 
                               ¨ 
                             
                             n 
                           
                            
                           
                             z 
                             
                               6 
                                
                               n 
                             
                           
                         
                         + 
                         
                           2 
                            
                           
                               
                           
                            
                           
                             
                               η 
                               . 
                             
                             n 
                           
                            
                           
                             
                               z 
                               . 
                             
                             
                               6 
                                
                               n 
                             
                           
                         
                         + 
                         
                           
                             α 
                             ¨ 
                           
                            
                           
                             ( 
                             
                               
                                 z 
                                 
                                   6 
                                    
                                   n 
                                 
                               
                               + 
                               
                                 E 
                                 1 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           2 
                            
                           
                               
                           
                            
                           
                             α 
                             . 
                           
                            
                           
                             
                               z 
                               . 
                             
                             
                               6 
                                
                               n 
                             
                           
                         
                         + 
                         
                           
                             β 
                             ¨ 
                           
                            
                           
                             a 
                             
                               
                                 1 
                                  
                                 n 
                               
                                
                               
                                   
                               
                             
                           
                            
                           
                             S 
                             
                               αγη 
                                
                               
                                   
                               
                                
                               n 
                             
                           
                         
                         - 
                         
                           
                             
                               z 
                               ¨ 
                             
                             0 
                           
                            
                           
                             S 
                             
                               αγη 
                                
                               
                                   
                               
                                
                               n 
                             
                           
                            
                           
                             C 
                             β 
                           
                         
                         + 
                         
                           
                             
                               α 
                               . 
                             
                             2 
                           
                            
                           
                             E 
                             2 
                           
                         
                         + 
                         
                           
                             
                               β 
                               . 
                             
                             2 
                           
                            
                           
                             B 
                             1 
                           
                            
                           
                             S 
                             
                               αγη 
                                
                               
                                   
                               
                                
                               n 
                             
                           
                         
                         - 
                         
                           g 
                            
                           
                               
                           
                            
                           
                             S 
                             
                               αγη 
                                
                               
                                   
                               
                                
                               n 
                             
                           
                            
                           
                             C 
                             β 
                           
                         
                       
                       } 
                     
                   
                   = 
                   
                     
                       
                         - 
                         
                           
                             λ 
                             
                               1 
                                
                               n 
                             
                           
                            
                           
                             ( 
                             
                               
                                 z 
                                 
                                   6 
                                    
                                   n 
                                 
                               
                               - 
                               
                                 d 
                                 
                                   1 
                                    
                                   n 
                                 
                               
                             
                             ) 
                           
                         
                       
                        
                       
                         C 
                         
                           η 
                            
                           
                               
                           
                            
                           n 
                         
                       
                     
                     + 
                     
                       
                         
                           λ 
                           
                             2 
                              
                             n 
                           
                         
                          
                         
                           ( 
                           
                             
                               z 
                               
                                 6 
                                  
                                 n 
                               
                             
                             - 
                             
                               d 
                               
                                 1 
                                  
                                 n 
                               
                             
                           
                           ) 
                         
                       
                        
                       
                         S 
                         
                           η 
                            
                           
                               
                           
                            
                           n 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5.101 
                   ) 
                 
               
             
             
               
                 ∴ 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     λ 
                     
                       1 
                        
                       n 
                     
                   
                   = 
                   
                     
                       
                           
                       
                        
                       
                         
                           
                             
                               
                                 
                                   m 
                                   sn 
                                 
                                  
                                 
                                   z 
                                   
                                     6 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   { 
                                   
                                     
                                       
                                         
                                           η 
                                           ¨ 
                                         
                                         n 
                                       
                                        
                                       
                                         z 
                                         
                                           6 
                                            
                                           n 
                                         
                                       
                                     
                                     + 
                                     
                                       2 
                                        
                                       
                                         
                                           η 
                                           . 
                                         
                                         n 
                                       
                                        
                                       
                                         
                                           z 
                                           . 
                                         
                                         
                                           6 
                                            
                                           n 
                                         
                                       
                                     
                                     + 
                                     
                                       
                                         α 
                                         ¨ 
                                       
                                        
                                       
                                         ( 
                                         
                                           
                                             z 
                                             
                                               6 
                                                
                                               n 
                                             
                                           
                                           + 
                                           
                                             E 
                                             1 
                                           
                                         
                                         ) 
                                       
                                     
                                     + 
                                     
                                       2 
                                        
                                       
                                         α 
                                         . 
                                       
                                        
                                       
                                         
                                           z 
                                           . 
                                         
                                         
                                           6 
                                            
                                           n 
                                         
                                       
                                     
                                     + 
                                     
                                       
                                         β 
                                         ¨ 
                                       
                                        
                                       
                                         a 
                                         
                                           1 
                                            
                                           n 
                                         
                                       
                                        
                                       
                                         S 
                                         
                                           αγη 
                                            
                                           
                                               
                                           
                                            
                                           n 
                                         
                                       
                                     
                                     - 
                                     
                                       
                                         
                                           z 
                                           ¨ 
                                         
                                         0 
                                       
                                        
                                       
                                         S 
                                         
                                           αγη 
                                            
                                           
                                               
                                           
                                            
                                           n 
                                         
                                       
                                        
                                       
                                         C 
                                         β 
                                       
                                     
                                     + 
                                     
                                       
                                         
                                           α 
                                           . 
                                         
                                         2 
                                       
                                        
                                       
                                         E 
                                         2 
                                       
                                     
                                     + 
                                     
                                       
                                         
                                           β 
                                           . 
                                         
                                         2 
                                       
                                        
                                       
                                         β 
                                         1 
                                       
                                        
                                       
                                         S 
                                         
                                           αγη 
                                            
                                           
                                               
                                           
                                            
                                           n 
                                         
                                       
                                     
                                     - 
                                     
                                       g 
                                        
                                       
                                           
                                       
                                        
                                       
                                         S 
                                         
                                           αγη 
                                            
                                           
                                               
                                           
                                            
                                           n 
                                         
                                       
                                        
                                       
                                         C 
                                         β 
                                       
                                     
                                   
                                   } 
                                 
                               
                               - 
                             
                           
                         
                         
                           
                             
                               
                                 
                                   λ 
                                   
                                     2 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       z 
                                       
                                         6 
                                          
                                         n 
                                       
                                     
                                     - 
                                     
                                       d 
                                       
                                         1 
                                          
                                         n 
                                       
                                     
                                   
                                   ) 
                                 
                               
                                
                               
                                 S 
                                 
                                   η 
                                    
                                   
                                       
                                   
                                    
                                   n 
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         - 
                         
                           ( 
                           
                             
                               z 
                               
                                 6 
                                  
                                 n 
                               
                             
                             - 
                             
                               d 
                               
                                 1 
                                  
                                 n 
                               
                             
                           
                           ) 
                         
                       
                        
                       
                         C 
                         
                           η 
                            
                           
                               
                           
                            
                           n 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5.102 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                            
                           
                              
                             t 
                           
                         
                          
                         
                           ( 
                           
                             
                               ∂ 
                               L 
                             
                             
                               ∂ 
                               
                                 
                                   θ 
                                   . 
                                 
                                 n 
                               
                             
                           
                           ) 
                         
                       
                       - 
                       
                         
                           ∂ 
                           L 
                         
                         
                           ∂ 
                           
                             θ 
                             n 
                           
                         
                       
                     
                     = 
                     
                       
                         
                           
                             ∂ 
                             F 
                           
                           
                             ∂ 
                             
                               
                                 θ 
                                 . 
                               
                               n 
                             
                           
                         
                         + 
                         
                           
                             ∑ 
                             
                               l 
                               , 
                               n 
                             
                           
                            
                           
                             
                               λ 
                               
                                 l 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                              
                             
                               a 
                               
                                 l 
                                  
                                 
                                     
                                 
                                  
                                 n 
                                  
                                 
                                     
                                 
                                  
                                 4 
                               
                             
                              
                             
                                 
                             
                              
                             l 
                           
                         
                       
                       = 
                       1 
                     
                   
                   , 
                   2 
                   , 
                   
                     
                       3 
                        
                       
                           
                       
                        
                       n 
                     
                     = 
                     i 
                   
                   , 
                   ii 
                   , 
                   iii 
                   , 
                   iv 
                 
               
               
                 
                   ( 
                   5.103 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         θ 
                         ¨ 
                       
                       n 
                     
                      
                     
                       m 
                       aw2In 
                     
                   
                   + 
                   
                     
                       α 
                       ¨ 
                     
                     [ 
                     
                       
                         
                           m 
                           aw2In 
                         
                         - 
                         
                           
                             m 
                             aw1n 
                           
                            
                           
                             { 
                             
                               
                                 
                                   c 
                                   
                                     2 
                                      
                                     n 
                                   
                                 
                                  
                                 sin 
                                  
                                 
                                     
                                 
                                  
                                 
                                   θ 
                                   n 
                                 
                               
                               - 
                               
                                 
                                   b 
                                   
                                     2 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   cos 
                                    
                                   
                                     ( 
                                     
                                       
                                         γ 
                                         n 
                                       
                                       + 
                                       
                                         θ 
                                         n 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                             } 
                           
                         
                         - 
                         
                           
                             α 
                             . 
                           
                            
                           
                             
                               θ 
                               . 
                             
                             n 
                           
                            
                           
                             m 
                             aw1n 
                           
                            
                           
                             { 
                             
                               
                                 
                                   c 
                                   
                                     2 
                                      
                                     n 
                                   
                                 
                                  
                                 cos 
                                  
                                 
                                     
                                 
                                  
                                 
                                   θ 
                                   n 
                                 
                               
                               + 
                               
                                 
                                   b 
                                   
                                     2 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         γ 
                                         n 
                                       
                                       + 
                                       
                                         θ 
                                         n 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                             } 
                           
                         
                         - 
                         
                           
                             β 
                             ¨ 
                           
                            
                           
                             m 
                             aw1n 
                           
                            
                           
                             a 
                             
                               1 
                                
                               n 
                             
                           
                            
                           
                             cos 
                              
                             
                               ( 
                               
                                 α 
                                 + 
                                 
                                   γ 
                                   n 
                                 
                                 + 
                                 
                                   θ 
                                   n 
                                 
                               
                               ) 
                             
                           
                         
                         + 
                         
                           
                             
                               β 
                               . 
                             
                              
                             
                               ( 
                               
                                 
                                   α 
                                   . 
                                 
                                 + 
                                 
                                   
                                     θ 
                                     . 
                                   
                                   n 
                                 
                               
                               ) 
                             
                           
                            
                           
                             m 
                             aw1n 
                           
                            
                           
                             a 
                             
                               1 
                                
                               n 
                             
                           
                            
                           
                             sin 
                              
                             
                               ( 
                               
                                 α 
                                 + 
                                 
                                   γ 
                                   n 
                                 
                                 + 
                                 
                                   θ 
                                   n 
                                 
                               
                               ) 
                             
                           
                         
                         + 
                         
                           
                             
                               z 
                               ¨ 
                             
                             0 
                           
                            
                           
                             m 
                             aw1n 
                           
                            
                           
                             cos 
                              
                             
                               ( 
                               
                                 α 
                                 + 
                                 
                                   γ 
                                   n 
                                 
                                 + 
                                 
                                   θ 
                                   n 
                                 
                               
                               ) 
                             
                           
                            
                           cos 
                            
                           
                               
                           
                            
                           β 
                         
                         - 
                         
                           
                             ( 
                             
                               
                                 α 
                                 . 
                               
                               + 
                               
                                 
                                   θ 
                                   . 
                                 
                                 n 
                               
                             
                             ) 
                           
                            
                           
                             
                               z 
                               . 
                             
                             0 
                           
                            
                           
                             m 
                             aw1n 
                           
                            
                           
                             sin 
                              
                             
                               ( 
                               
                                 α 
                                 + 
                                 
                                   γ 
                                   n 
                                 
                                 + 
                                 
                                   θ 
                                   n 
                                 
                               
                               ) 
                             
                           
                            
                           cos 
                            
                           
                               
                           
                            
                           β 
                         
                         - 
                         
                           
                             β 
                             . 
                           
                            
                           
                             
                               z 
                               . 
                             
                             0 
                           
                            
                           
                             m 
                             aw1n 
                           
                            
                           
                             cos 
                              
                             
                               ( 
                               
                                 α 
                                 + 
                                 
                                   γ 
                                   n 
                                 
                                 + 
                                 
                                   θ 
                                   n 
                                 
                               
                               ) 
                             
                           
                            
                           sin 
                            
                           
                               
                           
                            
                           β 
                         
                         - 
                         
                           [ 
                           
                             
                               
                                 - 
                                 
                                   k 
                                   zi 
                                 
                               
                                
                               
                                 e 
                                 
                                   0 
                                    
                                   i 
                                 
                                 2 
                               
                                
                               
                                 { 
                                 
                                   
                                     sin 
                                      
                                     
                                       ( 
                                       
                                         
                                           γ 
                                           i 
                                         
                                         + 
                                         
                                           θ 
                                           i 
                                         
                                       
                                       ) 
                                     
                                   
                                   - 
                                   
                                     sin 
                                      
                                     
                                       ( 
                                       
                                         
                                           y 
                                           ii 
                                         
                                         + 
                                         
                                           θ 
                                           ii 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                 } 
                               
                                
                               
                                 cos 
                                  
                                 
                                   ( 
                                   
                                     
                                       γ 
                                       n 
                                     
                                     + 
                                     
                                       θ 
                                       n 
                                     
                                   
                                   ) 
                                 
                               
                                
                               
                                 X 
                                 s 
                               
                             
                             - 
                             
                               
                                 k 
                                 ziii 
                               
                                
                               
                                 e 
                                 
                                   0 
                                    
                                   iii 
                                 
                                 2 
                               
                                
                               
                                 { 
                                 
                                   
                                     sin 
                                      
                                     
                                       ( 
                                       
                                         
                                           γ 
                                           iii 
                                         
                                         + 
                                         
                                           θ 
                                           iii 
                                         
                                       
                                       ) 
                                     
                                   
                                   - 
                                   
                                     sin 
                                      
                                     
                                       ( 
                                       
                                         
                                           γ 
                                           iv 
                                         
                                         + 
                                         
                                           θ 
                                           iv 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                 } 
                               
                                
                               
                                 cos 
                                  
                                 
                                   ( 
                                   
                                     
                                       γ 
                                       n 
                                     
                                     + 
                                     
                                       θ 
                                       n 
                                     
                                   
                                   ) 
                                 
                               
                                
                               
                                 X 
                                 s 
                               
                             
                             - 
                             
                               
                                 
                                   α 
                                   . 
                                 
                                 2 
                               
                                
                               
                                 m 
                                 aw1n 
                               
                                
                               
                                 { 
                                 
                                   
                                     
                                       c 
                                       
                                         
                                           2 
                                            
                                           n 
                                         
                                          
                                         
                                             
                                         
                                       
                                     
                                      
                                     cos 
                                      
                                     
                                         
                                     
                                      
                                     
                                       θ 
                                       n 
                                     
                                   
                                   + 
                                   
                                     
                                       b 
                                       
                                         2 
                                          
                                         n 
                                       
                                     
                                      
                                     
                                       sin 
                                        
                                       
                                         ( 
                                         
                                           
                                             γ 
                                             n 
                                           
                                           + 
                                           
                                             θ 
                                             n 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                 
                                 } 
                               
                             
                             + 
                             
                               
                                 
                                   β 
                                   . 
                                 
                                 2 
                               
                                
                               
                                 〈 
                                 
                                   
                                     
                                       m 
                                       an 
                                     
                                      
                                     
                                       { 
                                       
                                         
                                           
                                             e 
                                             
                                               1 
                                                
                                               n 
                                             
                                           
                                            
                                           
                                             sin 
                                              
                                             
                                               ( 
                                               
                                                 α 
                                                 + 
                                                 
                                                   γ 
                                                   n 
                                                 
                                                 + 
                                                 
                                                   θ 
                                                   n 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                         + 
                                         
                                           
                                             c 
                                             
                                               2 
                                                
                                               n 
                                             
                                           
                                            
                                           
                                             cos 
                                              
                                             
                                               ( 
                                               
                                                 α 
                                                 + 
                                                 
                                                   γ 
                                                   n 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                         + 
                                         
                                           
                                             b 
                                             
                                               2 
                                                
                                               n 
                                             
                                           
                                            
                                           sin 
                                            
                                           
                                               
                                           
                                            
                                           α 
                                         
                                       
                                       } 
                                     
                                      
                                     
                                       e 
                                       
                                         1 
                                          
                                         n 
                                       
                                     
                                      
                                     
                                       cos 
                                        
                                       
                                         ( 
                                         
                                           α 
                                           + 
                                           
                                             γ 
                                             n 
                                           
                                           + 
                                           
                                             θ 
                                             n 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                   + 
                                   
                                     
                                       m 
                                       wn 
                                     
                                      
                                     
                                       { 
                                       
                                         
                                           
                                             e 
                                             
                                               
                                                 3 
                                                  
                                                 n 
                                               
                                                
                                               
                                                   
                                               
                                             
                                           
                                            
                                           
                                             sin 
                                              
                                             
                                               ( 
                                               
                                                 α 
                                                 + 
                                                 
                                                   γ 
                                                   n 
                                                 
                                                 + 
                                                 
                                                   θ 
                                                   n 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                         + 
                                         
                                           
                                             c 
                                             
                                               2 
                                                
                                               n 
                                             
                                           
                                            
                                           
                                             cos 
                                              
                                             
                                               ( 
                                               
                                                 α 
                                                 + 
                                                 
                                                   γ 
                                                   n 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                         + 
                                         
                                           
                                             b 
                                             
                                               2 
                                                
                                               n 
                                             
                                           
                                            
                                           sin 
                                            
                                           
                                               
                                           
                                            
                                           α 
                                         
                                       
                                       } 
                                     
                                      
                                     
                                       e 
                                       
                                         3 
                                          
                                         n 
                                       
                                     
                                      
                                     
                                       cos 
                                        
                                       
                                         ( 
                                         
                                           α 
                                           + 
                                           
                                             γ 
                                             n 
                                           
                                           + 
                                           
                                             θ 
                                             n 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                 
                                 〉 
                               
                             
                             - 
                             
                               
                                 θ 
                                 . 
                               
                                
                               
                                 α 
                                 . 
                               
                                
                               
                                 m 
                                 aw1n 
                               
                                
                               
                                 { 
                                 
                                   
                                     
                                       c 
                                       
                                         2 
                                          
                                         n 
                                       
                                     
                                      
                                     cos 
                                      
                                     
                                         
                                     
                                      
                                     
                                       θ 
                                       n 
                                     
                                   
                                   + 
                                   
                                     
                                       b 
                                       
                                         2 
                                          
                                         n 
                                       
                                     
                                      
                                     
                                       sin 
                                        
                                       
                                         ( 
                                         
                                           
                                             γ 
                                             n 
                                           
                                           + 
                                           
                                             θ 
                                             n 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                 
                                 } 
                               
                             
                             + 
                             
                               
                                 θ 
                                 . 
                               
                                
                               
                                 β 
                                 . 
                               
                                
                               
                                 m 
                                 aw1n 
                               
                                
                               
                                 a 
                                 
                                   1 
                                    
                                   n 
                                 
                               
                                
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     α 
                                     + 
                                     
                                       γ 
                                       n 
                                     
                                     + 
                                     
                                       θ 
                                       n 
                                     
                                   
                                   ) 
                                 
                               
                             
                             + 
                             
                               
                                 α 
                                 . 
                               
                                
                               
                                 β 
                                 . 
                               
                                
                               
                                 a 
                                 
                                   1 
                                    
                                   n 
                                 
                               
                                
                               
                                 m 
                                 aw1n 
                               
                                
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     α 
                                     + 
                                     
                                       γ 
                                       n 
                                     
                                     + 
                                     
                                       θ 
                                       n 
                                     
                                   
                                   ) 
                                 
                               
                             
                             - 
                             
                               
                                 gm 
                                 aw1n 
                               
                                
                               
                                 cos 
                                  
                                 
                                   ( 
                                   
                                     α 
                                     + 
                                     
                                       γ 
                                       n 
                                     
                                     + 
                                     
                                       θ 
                                       n 
                                     
                                   
                                   ) 
                                 
                               
                                
                               cos 
                                
                               
                                   
                               
                                
                               β 
                             
                             - 
                             
                               
                                 
                                   
                                     z 
                                     . 
                                   
                                   0 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       α 
                                       . 
                                     
                                     + 
                                     
                                       
                                         θ 
                                         . 
                                       
                                       n 
                                     
                                   
                                   ) 
                                 
                               
                                
                               
                                 m 
                                 aw1n 
                               
                                
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     α 
                                     + 
                                     
                                       γ 
                                       n 
                                     
                                     + 
                                     
                                       θ 
                                       n 
                                     
                                   
                                   ) 
                                 
                               
                                
                               cos 
                                
                               
                                   
                               
                                
                               β 
                             
                             - 
                             
                               
                                 β 
                                 . 
                               
                                
                               
                                 
                                   z 
                                   . 
                                 
                                 0 
                               
                                
                               
                                 m 
                                 aw1n 
                               
                                
                               
                                 cos 
                                  
                                 
                                   ( 
                                   
                                     α 
                                     + 
                                     
                                       γ 
                                       n 
                                     
                                     + 
                                     
                                       θ 
                                       n 
                                     
                                   
                                   ) 
                                 
                               
                                
                               sin 
                                
                               
                                   
                               
                                
                               β 
                             
                           
                           ] 
                         
                       
                       = 
                       
                         
                           
                             λ 
                             
                               1 
                                
                               n 
                             
                           
                            
                           
                             e 
                             
                               2 
                                
                               n 
                             
                           
                            
                           sin 
                            
                           
                               
                           
                            
                           
                             θ 
                             n 
                           
                         
                         + 
                         
                           
                             λ 
                             
                               2 
                                
                               n 
                             
                           
                            
                           
                             e 
                             
                               2 
                                
                               n 
                             
                           
                            
                           cos 
                            
                           
                               
                           
                            
                           
                             θ 
                             n 
                           
                         
                         + 
                         
                           
                             λ 
                             
                               3 
                                
                               n 
                             
                           
                            
                           
                             e 
                             
                               3 
                                
                               n 
                             
                           
                            
                           
                             cos 
                              
                             
                               ( 
                               
                                 α 
                                 + 
                                 
                                   γ 
                                   n 
                                 
                                 + 
                                 
                                   θ 
                                   n 
                                 
                               
                               ) 
                             
                           
                            
                           cos 
                            
                           
                               
                           
                            
                           β 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5.104 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           θ 
                           ¨ 
                         
                         n 
                       
                        
                       
                         m 
                         aw2In 
                       
                     
                     + 
                     
                       
                         α 
                         ¨ 
                       
                        
                       
                         ( 
                         
                           
                             m 
                             aw2In 
                           
                           - 
                           
                             
                               m 
                               aw1n 
                             
                              
                             
                               H 
                               1 
                             
                           
                         
                         ) 
                       
                     
                     - 
                     
                       
                         α 
                         . 
                       
                        
                       
                         
                           θ 
                           . 
                         
                         n 
                       
                        
                       
                         m 
                         aw1n 
                       
                        
                       
                         H 
                         2 
                       
                     
                     - 
                     
                       
                         β 
                         ¨ 
                       
                        
                       
                         m 
                         aw1n 
                       
                        
                       
                         a 
                         
                           1 
                            
                           n 
                         
                       
                        
                       
                         C 
                         
                           αγθ 
                            
                           
                               
                           
                            
                           n 
                         
                       
                     
                     + 
                     
                       
                         
                           β 
                           . 
                         
                          
                         
                           ( 
                           
                             
                               α 
                               . 
                             
                             + 
                             
                               
                                 θ 
                                 . 
                               
                               n 
                             
                           
                           ) 
                         
                       
                        
                       
                         m 
                         aw1n 
                       
                        
                       
                         a 
                         
                           1 
                            
                           n 
                         
                       
                        
                       
                         S 
                         
                           αγθ 
                            
                           
                               
                           
                            
                           n 
                         
                       
                     
                     + 
                     
                       
                         
                           z 
                           ¨ 
                         
                         0 
                       
                        
                       
                         m 
                         aw1n 
                       
                        
                       
                         C 
                         
                           αγθ 
                            
                           
                               
                           
                            
                           n 
                         
                       
                        
                       
                         C 
                         β 
                       
                     
                     - 
                     
                       [ 
                       
                         
                           
                             - 
                             
                               k 
                               zi 
                             
                           
                            
                           
                             e 
                             
                               0 
                                
                               i 
                             
                             2 
                           
                            
                           
                             { 
                             
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       γ 
                                       i 
                                     
                                     + 
                                     
                                       θ 
                                       i 
                                     
                                   
                                   ) 
                                 
                               
                               + 
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       γ 
                                       ii 
                                     
                                     + 
                                     
                                       θ 
                                       ii 
                                     
                                   
                                   ) 
                                 
                               
                             
                             } 
                           
                            
                           
                             X 
                             s 
                           
                         
                         - 
                         
                           
                             k 
                             ziii 
                           
                            
                           
                             e 
                             
                               0 
                                
                               iii 
                             
                             2 
                           
                            
                           
                             { 
                             
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       γ 
                                       iii 
                                     
                                     + 
                                     
                                       θ 
                                       iii 
                                     
                                   
                                   ) 
                                 
                               
                               + 
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       γ 
                                       iv 
                                     
                                     + 
                                     
                                       θ 
                                       iv 
                                     
                                   
                                   ) 
                                 
                               
                             
                             } 
                           
                            
                           
                             cos 
                              
                             
                               ( 
                               
                                 
                                   γ 
                                   n 
                                 
                                 + 
                                 
                                   θ 
                                   
                                     n 
                                      
                                     
                                         
                                     
                                   
                                 
                               
                               ) 
                             
                           
                            
                           
                             X 
                             s 
                           
                         
                         - 
                         
                           
                             
                               α 
                               . 
                             
                             2 
                           
                            
                           
                             m 
                             aw1n 
                           
                            
                           
                             H 
                             2 
                           
                         
                         + 
                         
                           
                             
                               β 
                               . 
                             
                             2 
                           
                            
                           
                             ( 
                             
                               
                                 
                                   m 
                                   an 
                                 
                                  
                                 
                                   B 
                                   2 
                                 
                                  
                                 
                                   e 
                                   
                                     1 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   C 
                                   
                                     αγθ 
                                      
                                     
                                         
                                     
                                      
                                     n 
                                   
                                 
                               
                               + 
                               
                                 
                                   m 
                                   wn 
                                 
                                  
                                 
                                   B 
                                   3 
                                 
                                  
                                 
                                   e 
                                   
                                     3 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   C 
                                   
                                     αγθ 
                                      
                                     
                                         
                                     
                                      
                                     n 
                                   
                                 
                               
                             
                             ) 
                           
                         
                         - 
                         
                           
                             θ 
                             . 
                           
                            
                           
                             α 
                             . 
                           
                            
                           
                             m 
                             aw1n 
                           
                            
                           
                             H 
                             2 
                           
                         
                         + 
                         
                           
                             θ 
                             . 
                           
                            
                           
                             β 
                             . 
                           
                            
                           
                             m 
                             aw1n 
                           
                            
                           
                             a 
                             
                               1 
                                
                               n 
                             
                           
                            
                           
                             S 
                             
                               
                                 αγθ 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                                
                               
                                   
                               
                             
                           
                         
                         + 
                         
                           
                             α 
                             . 
                           
                            
                           
                             β 
                             . 
                           
                            
                           
                             a 
                             
                               1 
                                
                               n 
                             
                           
                            
                           
                             m 
                             aw1n 
                           
                            
                           
                             S 
                             
                               αγθ 
                                
                               
                                   
                               
                                
                               n 
                             
                           
                         
                         - 
                         
                           
                             gm 
                             aw1n 
                           
                            
                           
                             C 
                             
                               αγθ 
                                
                               
                                   
                               
                                
                               n 
                             
                           
                            
                           
                             C 
                             β 
                           
                         
                       
                       ] 
                     
                   
                   = 
                   
                     
                       
                         λ 
                         
                           1 
                            
                           n 
                         
                       
                        
                       
                         e 
                         
                           2 
                            
                           n 
                         
                       
                        
                       
                         S 
                         
                           θ 
                            
                           
                               
                           
                            
                           n 
                         
                       
                     
                     + 
                     
                       
                         λ 
                         
                           2 
                            
                           n 
                         
                       
                        
                       
                         e 
                         
                           2 
                            
                           n 
                         
                       
                        
                       
                         C 
                         
                           θ 
                            
                           
                               
                           
                            
                           n 
                         
                       
                     
                     + 
                     
                       
                         λ 
                         
                           3 
                            
                           n 
                         
                       
                        
                       
                         e 
                         
                           3 
                            
                           n 
                         
                       
                        
                       
                         C 
                         
                           αγθ 
                            
                           
                               
                           
                            
                           n 
                         
                       
                        
                       
                         C 
                         β 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5.105 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           θ 
                           ¨ 
                         
                         n 
                       
                        
                       
                         m 
                         aw2In 
                       
                     
                     + 
                     
                       
                         α 
                         ¨ 
                       
                        
                       
                         ( 
                         
                           
                             m 
                             aw2In 
                           
                           - 
                           
                             
                               m 
                               aw1n 
                             
                              
                             
                               H 
                               1 
                             
                           
                         
                         ) 
                       
                     
                     - 
                     
                       
                         β 
                         ¨ 
                       
                        
                       
                         m 
                         
                           aw 
                            
                           
                               
                           
                            
                           1 
                            
                           n 
                         
                       
                        
                       
                         a 
                         
                           1 
                            
                           n 
                         
                       
                        
                       
                         C 
                         
                           αγθ 
                            
                           
                               
                           
                            
                           n 
                         
                       
                     
                     + 
                     
                       
                         
                           z 
                           ¨ 
                         
                         0 
                       
                        
                       
                         m 
                         aw1n 
                       
                        
                       
                         C 
                         
                           αγθ 
                            
                           
                               
                           
                            
                           n 
                         
                       
                        
                       
                         C 
                         β 
                       
                     
                     + 
                     
                       
                         
                           α 
                           . 
                         
                         2 
                       
                        
                       
                         m 
                         aw1n 
                       
                        
                       
                         H 
                         2 
                       
                     
                     - 
                     
                       
                         
                           β 
                           . 
                         
                         2 
                       
                        
                       
                         ( 
                         
                           
                             
                               m 
                               an 
                             
                              
                             
                               B 
                               2 
                             
                              
                             
                               e 
                               
                                 1 
                                  
                                 n 
                               
                             
                              
                             
                               C 
                               
                                 αγθ 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                           
                           + 
                           
                             
                               m 
                               wn 
                             
                              
                             
                               B 
                               3 
                             
                              
                             
                               e 
                               
                                 3 
                                  
                                 n 
                               
                             
                              
                             
                               C 
                               
                                 αγθ 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                           
                         
                         ) 
                       
                     
                     + 
                     
                       
                         gm 
                         aw1n 
                       
                        
                       
                         C 
                         
                           αγθ 
                            
                           
                               
                           
                            
                           n 
                         
                       
                        
                       
                         C 
                         β 
                       
                     
                     + 
                     
                       
                         k 
                         zi 
                       
                        
                       
                         e 
                         
                           0 
                            
                           i 
                         
                         2 
                       
                        
                       
                         { 
                         
                           
                             sin 
                              
                             
                               ( 
                               
                                 
                                   γ 
                                   i 
                                 
                                 + 
                                 
                                   θ 
                                   i 
                                 
                               
                               ) 
                             
                           
                           + 
                           
                             sin 
                              
                             
                               ( 
                               
                                 
                                   γ 
                                   ii 
                                 
                                 + 
                                 
                                   θ 
                                   ii 
                                 
                               
                               ) 
                             
                           
                         
                         } 
                       
                        
                       
                         cos 
                          
                         
                           ( 
                           
                             
                               γ 
                               n 
                             
                             + 
                             
                               θ 
                               n 
                             
                           
                           ) 
                         
                       
                     
                     + 
                     
                       
                         k 
                         ziii 
                       
                        
                       
                         e 
                         
                           0 
                            
                           iii 
                         
                         2 
                       
                        
                       
                         { 
                         
                           
                             sin 
                              
                             
                               ( 
                               
                                 
                                   γ 
                                   iii 
                                 
                                 + 
                                 
                                   θ 
                                   iii 
                                 
                               
                               ) 
                             
                           
                           + 
                           
                             sin 
                              
                             
                               ( 
                               
                                 
                                   γ 
                                   iv 
                                 
                                 + 
                                 
                                   θ 
                                   iv 
                                 
                               
                               ) 
                             
                           
                         
                         } 
                       
                        
                       
                         cos 
                          
                         
                           ( 
                           
                             
                               γ 
                               n 
                             
                             + 
                             
                               θ 
                               n 
                             
                           
                           ) 
                         
                       
                     
                   
                   = 
                   
                     
                       
                         λ 
                         
                           1 
                            
                           n 
                         
                       
                        
                       
                         e 
                         
                           2 
                            
                           n 
                         
                       
                        
                       
                         S 
                         
                           θ 
                            
                           
                               
                           
                            
                           n 
                         
                       
                     
                     + 
                     
                       
                         λ 
                         
                           2 
                            
                           n 
                         
                       
                        
                       
                         e 
                         
                           2 
                            
                           n 
                         
                       
                        
                       
                         C 
                         
                           θ 
                            
                           
                               
                           
                            
                           n 
                         
                       
                     
                     + 
                     
                       
                         λ 
                         
                           3 
                            
                           n 
                         
                       
                        
                       
                         e 
                         
                           3 
                            
                           n 
                         
                       
                        
                       
                         C 
                         
                           αγθ 
                            
                           
                               
                           
                            
                           n 
                         
                       
                        
                       
                         C 
                         β 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5.106 
                   ) 
                 
               
             
             
               
                 ∴ 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       θ 
                       ¨ 
                     
                     n 
                   
                   = 
                   
                     
                       
                         
                           
                             α 
                             ¨ 
                           
                            
                           
                             ( 
                             
                               
                                 m 
                                 aw2In 
                               
                               - 
                               
                                 
                                   m 
                                   aw1n 
                                 
                                  
                                 
                                   H 
                                   1 
                                 
                               
                             
                             ) 
                           
                         
                         - 
                         
                           
                             β 
                             ¨ 
                           
                            
                           
                             m 
                             aw1n 
                           
                            
                           
                             a 
                             
                               1 
                                
                               n 
                             
                           
                            
                           
                             C 
                             
                               αγθ 
                                
                               
                                   
                               
                                
                               n 
                             
                           
                         
                         + 
                         
                           
                             
                               z 
                               ¨ 
                             
                             0 
                           
                            
                           
                             m 
                             aw1n 
                           
                            
                           
                             C 
                             
                               αγθ 
                                
                               
                                   
                               
                                
                               n 
                             
                           
                            
                           
                             C 
                             β 
                           
                         
                         + 
                         
                           
                             
                               α 
                               . 
                             
                             2 
                           
                            
                           
                             m 
                             aww1n 
                           
                            
                           
                             H 
                             2 
                           
                         
                         - 
                         
                           
 
                         
                          
                         
                             
                         
                          
                         
                           
                             
                               β 
                               . 
                             
                             2 
                           
                            
                           
                             ( 
                             
                               
                                 
                                   m 
                                   an 
                                 
                                  
                                 
                                   B 
                                   2 
                                 
                                  
                                 
                                   e 
                                   
                                     1 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   C 
                                   
                                     αγθ 
                                      
                                     
                                         
                                     
                                      
                                     n 
                                   
                                 
                               
                               + 
                               
                                 
                                   m 
                                   wn 
                                 
                                  
                                 
                                   B 
                                   3 
                                 
                                  
                                 
                                   e 
                                   
                                     3 
                                      
                                     n 
                                   
                                 
                                  
                                 
                                   C 
                                   
                                     αγθ 
                                      
                                     
                                         
                                     
                                      
                                     n 
                                   
                                 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           
                             gm 
                             aw1n 
                           
                            
                           
                             C 
                             
                               αγθ 
                                
                               
                                   
                               
                                
                               n 
                             
                           
                            
                           
                             C 
                             β 
                           
                         
                         - 
                         
                           
                             λ 
                             
                               1 
                                
                               n 
                             
                           
                            
                           
                             e 
                             
                               2 
                                
                               n 
                             
                           
                            
                           
                             S 
                             
                               θ 
                                
                               
                                   
                               
                                
                               n 
                             
                           
                         
                         - 
                         
                           
 
                         
                          
                         
                             
                         
                          
                         
                           
                             λ 
                             
                               2 
                                
                               n 
                             
                           
                            
                           
                             e 
                             
                               2 
                                
                               n 
                             
                           
                            
                           
                             C 
                             
                               θ 
                                
                               
                                   
                               
                                
                               n 
                             
                           
                         
                         - 
                         
                           
                             λ 
                             
                               3 
                                
                               n 
                             
                           
                            
                           
                             e 
                             
                               
                                 3 
                                  
                                 n 
                               
                                
                               
                                   
                               
                             
                           
                            
                           
                             C 
                             
                               αγθ 
                                
                               
                                   
                               
                                
                               n 
                             
                           
                         
                         + 
                         
                           C 
                           β 
                         
                         + 
                         
                           
                             k 
                             zi 
                           
                            
                           
                             e 
                             
                               0 
                                
                               i 
                             
                             2 
                           
                            
                           
                             { 
                             
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       γ 
                                       i 
                                     
                                     + 
                                     
                                       θ 
                                       i 
                                     
                                   
                                   ) 
                                 
                               
                               + 
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       γ 
                                       ii 
                                     
                                     + 
                                     
                                       θ 
                                       ii 
                                     
                                   
                                   ) 
                                 
                               
                             
                             } 
                           
                         
                       
                        
                       
                         
 
                       
                        
                       
                           
                       
                        
                       
                         
                           cos 
                            
                           
                             ( 
                             
                               
                                 γ 
                                 n 
                               
                               + 
                               
                                 θ 
                                 n 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           
                             k 
                             ziii 
                           
                            
                           
                             e 
                             
                               0 
                                
                               iii 
                             
                             2 
                           
                            
                           
                             { 
                             
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       γ 
                                       iii 
                                     
                                     + 
                                     
                                       θ 
                                       iii 
                                     
                                   
                                   ) 
                                 
                               
                               + 
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       γ 
                                       iv 
                                     
                                     + 
                                     
                                       θ 
                                       iv 
                                     
                                   
                                   ) 
                                 
                               
                             
                             } 
                           
                            
                           
                             cos 
                              
                             
                               ( 
                               
                                 
                                   γ 
                                   n 
                                 
                                 + 
                                 
                                   θ 
                                   n 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                     
                       - 
                       
                         m 
                         aw2In 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5.107 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                            
                           
                              
                             t 
                           
                         
                          
                         
                           ( 
                           
                             
                               ∂ 
                               L 
                             
                             
                               ∂ 
                               
                                 
                                   z 
                                   . 
                                 
                                 
                                   6 
                                    
                                   n 
                                 
                               
                             
                           
                           ) 
                         
                       
                       - 
                       
                         
                           ∂ 
                           L 
                         
                         
                           ∂ 
                           
                             z 
                             
                               6 
                                
                               n 
                             
                           
                         
                       
                     
                     = 
                     
                       
                         
                           
                             ∂ 
                             F 
                           
                           
                             ∂ 
                             
                               
                                 z 
                                 . 
                               
                               
                                 6 
                                  
                                 n 
                               
                             
                           
                         
                         + 
                         
                           
                             ∑ 
                             
                               l 
                               , 
                               n 
                             
                           
                            
                           
                             
                               λ 
                               
                                 l 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                              
                             
                               a 
                               
                                 l 
                                  
                                 
                                     
                                 
                                  
                                 n 
                                  
                                 
                                     
                                 
                                  
                                 5 
                               
                             
                              
                             
                                 
                             
                              
                             l 
                           
                         
                       
                       = 
                       1 
                     
                   
                   , 
                   2 
                   , 
                   
                     
                       3 
                        
                       
                           
                       
                        
                       n 
                     
                     = 
                     i 
                   
                   , 
                   ii 
                   , 
                   iii 
                   , 
                   iv 
                 
               
               
                 
                   ( 
                   5.108 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           m 
                           sn 
                         
                          
                         
                           
                             z 
                             ¨ 
                           
                           
                             6 
                              
                             n 
                           
                         
                       
                       + 
                       
                         
                           α 
                           ¨ 
                         
                          
                         
                           m 
                           sn 
                         
                          
                         
                           { 
                           
                             
                               
                                 c 
                                 
                                   1 
                                    
                                   n 
                                 
                               
                                
                               sin 
                                
                               
                                   
                               
                                
                               
                                 η 
                                 n 
                               
                             
                             + 
                             
                               
                                 b 
                                 
                                   2 
                                    
                                   n 
                                 
                               
                                
                               
                                 cos 
                                  
                                 
                                   ( 
                                   
                                     
                                       γ 
                                       n 
                                     
                                     + 
                                     
                                       η 
                                       n 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           } 
                         
                       
                       + 
                       
                         
                           α 
                           . 
                         
                          
                         
                           
                             η 
                             . 
                           
                           n 
                         
                          
                         
                           m 
                           sn 
                         
                          
                         
                           { 
                           
                             
                               
                                 c 
                                 
                                   1 
                                    
                                   n 
                                 
                               
                                
                               cos 
                                
                               
                                   
                               
                                
                               
                                 η 
                                 
                                   n 
                                    
                                   
                                       
                                   
                                 
                               
                             
                             - 
                             
                               
                                 b 
                                 
                                   2 
                                    
                                   n 
                                 
                               
                                
                               
                                 sin 
                                  
                                 
                                   ( 
                                   
                                     
                                       γ 
                                       n 
                                     
                                     + 
                                     
                                       η 
                                       n 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           } 
                         
                       
                       - 
                       
                         
                           β 
                           ¨ 
                         
                          
                         
                           m 
                           sn 
                         
                          
                         
                           a 
                           
                             1 
                              
                             n 
                           
                         
                          
                         
                           cos 
                            
                           
                             ( 
                             
                               α 
                               + 
                               
                                 γ 
                                 n 
                               
                               + 
                               
                                 η 
                                 n 
                               
                             
                             ) 
                           
                         
                       
                       + 
                       
                         
                           
                             β 
                             . 
                           
                            
                           
                             ( 
                             
                               
                                 α 
                                 . 
                               
                               + 
                               
                                 
                                   η 
                                   . 
                                 
                                 n 
                               
                             
                             ) 
                           
                         
                          
                         
                           m 
                           sn 
                         
                          
                         
                           a 
                           
                             1 
                              
                             n 
                           
                         
                          
                         
                           sin 
                            
                           
                             ( 
                             
                               α 
                               + 
                               
                                 γ 
                                 n 
                               
                               + 
                               
                                 η 
                                 n 
                               
                             
                             ) 
                           
                         
                       
                       + 
                       
                         
                           
                             z 
                             ¨ 
                           
                           0 
                         
                          
                         
                           m 
                           sn 
                         
                          
                         
                           cos 
                            
                           
                             ( 
                             
                               α 
                               + 
                               
                                 γ 
                                 n 
                               
                               + 
                               
                                 η 
                                 n 
                               
                             
                             ) 
                           
                         
                          
                         cos 
                          
                         
                             
                         
                          
                         β 
                       
                       - 
                       
                         
                           ( 
                           
                             
                               α 
                               . 
                             
                             + 
                             
                               
                                 η 
                                 . 
                               
                               n 
                             
                           
                           ) 
                         
                          
                         
                           
                             z 
                             . 
                           
                           0 
                         
                          
                         
                           m 
                           sn 
                         
                          
                         
                           sin 
                            
                           
                             ( 
                             
                               α 
                               + 
                               
                                 γ 
                                 n 
                               
                               + 
                               
                                 η 
                                 n 
                               
                             
                             ) 
                           
                         
                          
                         cos 
                          
                         
                             
                         
                          
                         β 
                       
                       - 
                       
                         
                           β 
                           . 
                         
                          
                         
                           
                             z 
                             . 
                           
                           0 
                         
                          
                         
                           m 
                           sn 
                         
                          
                         
                           cos 
                            
                           
                             ( 
                             
                               α 
                               + 
                               
                                 γ 
                                 n 
                               
                               + 
                               
                                 η 
                                 n 
                               
                             
                             ) 
                           
                         
                          
                         sin 
                          
                         
                             
                         
                          
                         β 
                       
                       - 
                       
                         〈 
                         
                           
                             
                               m 
                               sn 
                             
                              
                             
                               
                                 η 
                                 . 
                               
                               n 
                               2 
                             
                              
                             
                               z 
                               
                                 6 
                                  
                                 n 
                               
                             
                           
                           + 
                           
                             
                               
                                 α 
                                 . 
                               
                               2 
                             
                              
                             
                               
                                 m 
                                 sn 
                               
                                
                               
                                 [ 
                                 
                                   
                                     z 
                                     
                                       6 
                                        
                                       n 
                                     
                                   
                                   + 
                                   
                                     { 
                                     
                                       
                                         
                                           c 
                                           
                                             1 
                                              
                                             n 
                                           
                                         
                                          
                                         cos 
                                          
                                         
                                             
                                         
                                          
                                         
                                           η 
                                           n 
                                         
                                       
                                       - 
                                       
                                         
                                           b 
                                           
                                             2 
                                              
                                             n 
                                           
                                         
                                          
                                         
                                           sin 
                                            
                                           
                                             ( 
                                             
                                               
                                                 γ 
                                                 n 
                                               
                                               + 
                                               
                                                 η 
                                                 n 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                     } 
                                   
                                 
                                 ] 
                               
                             
                           
                           + 
                           
                             
                               
                                 β 
                                 . 
                               
                               2 
                             
                              
                             
                               m 
                               sn 
                             
                              
                             
                               { 
                               
                                 
                                   
                                     z 
                                     
                                       6 
                                        
                                       n 
                                     
                                   
                                    
                                   
                                     cos 
                                      
                                     
                                       ( 
                                       
                                         α 
                                         + 
                                         
                                           γ 
                                           n 
                                         
                                         + 
                                         
                                           η 
                                           n 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     c 
                                     
                                       1 
                                        
                                       n 
                                     
                                   
                                    
                                   
                                     cos 
                                      
                                     
                                       ( 
                                       
                                         α 
                                         + 
                                         
                                           γ 
                                           n 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     b 
                                     
                                       2 
                                        
                                       n 
                                     
                                   
                                    
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   α 
                                 
                               
                               } 
                             
                              
                             
                               cos 
                                
                               
                                 ( 
                                 
                                   α 
                                   + 
                                   
                                     γ 
                                     n 
                                   
                                   + 
                                   
                                     η 
                                     n 
                                   
                                 
                                 ) 
                               
                             
                           
                           + 
                           
                             
                               
                                 η 
                                 . 
                               
                               n 
                             
                              
                             
                               α 
                               . 
                             
                              
                             
                               m 
                               sn 
                             
                              
                             
                               { 
                               
                                 
                                   2 
                                    
                                   
                                     z 
                                     
                                       6 
                                        
                                       n 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     c 
                                     
                                       1 
                                        
                                       n 
                                     
                                   
                                    
                                   cos 
                                    
                                   
                                       
                                   
                                    
                                   
                                     η 
                                     n 
                                   
                                 
                                 - 
                                 
                                   
                                     b 
                                     
                                       2 
                                        
                                       n 
                                     
                                   
                                    
                                   
                                     sin 
                                      
                                     
                                       ( 
                                       
                                         
                                           γ 
                                           n 
                                         
                                         + 
                                         
                                           η 
                                           n 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                               
                               } 
                             
                           
                           + 
                           
                             
                               
                                 η 
                                 . 
                               
                               n 
                             
                              
                             
                               β 
                               . 
                             
                              
                             
                               m 
                               sn 
                             
                              
                             
                               a 
                               
                                 1 
                                  
                                 n 
                               
                             
                              
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   α 
                                   + 
                                   
                                     γ 
                                     n 
                                   
                                   + 
                                   
                                     η 
                                     n 
                                   
                                 
                                 ) 
                               
                             
                           
                           + 
                           
                             
                               α 
                               . 
                             
                              
                             
                               β 
                               . 
                             
                              
                             
                               a 
                               
                                 1 
                                  
                                 n 
                               
                             
                              
                             
                               m 
                               sn 
                             
                              
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   α 
                                   + 
                                   
                                     γ 
                                     n 
                                   
                                   + 
                                   
                                     η 
                                     n 
                                   
                                 
                                 ) 
                               
                             
                           
                           - 
                           
                             
                               gm 
                               sn 
                             
                              
                             
                               cos 
                                
                               
                                 ( 
                                 
                                   α 
                                   + 
                                   
                                     γ 
                                     n 
                                   
                                   + 
                                   
                                     η 
                                     n 
                                   
                                 
                                 ) 
                               
                             
                              
                             cos 
                              
                             
                                 
                             
                              
                             β 
                           
                           - 
                           
                             
                               k 
                               sn 
                             
                              
                             
                               ( 
                               
                                 
                                   z 
                                   
                                     6 
                                      
                                     n 
                                   
                                 
                                 - 
                                 
                                   l 
                                   sn 
                                 
                               
                               ) 
                             
                           
                           + 
                           
                             
                               
                                 
                                   z 
                                   . 
                                 
                                 0 
                               
                                
                               
                                 ( 
                                 
                                   
                                     α 
                                     . 
                                   
                                   + 
                                   
                                     
                                       η 
                                       . 
                                     
                                     
                                       n 
                                        
                                       
                                           
                                       
                                     
                                   
                                 
                                 ) 
                               
                             
                              
                             
                               m 
                               sn 
                             
                              
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   α 
                                   + 
                                   
                                     γ 
                                     n 
                                   
                                   + 
                                   
                                     η 
                                     n 
                                   
                                 
                                 ) 
                               
                             
                              
                             cos 
                              
                             
                                 
                             
                              
                             β 
                           
                           - 
                           
                             
                               β 
                               . 
                             
                              
                             
                               
                                 z 
                                 . 
                               
                               0 
                             
                              
                             
                               m 
                               sn 
                             
                              
                             cos 
                             ( 
                             
                               α 
                               + 
                               
                                 γ 
                                 n 
                               
                               + 
                               
                                 
                                   η 
                                   n 
                                 
                                  
                                 sin 
                                  
                                 
                                     
                                 
                                  
                                 β 
                               
                             
                           
                         
                       
                     
                     〉 
                   
                   = 
                   
                     
                       
                         - 
                         
                           c 
                           sn 
                         
                       
                        
                       
                         
                           z 
                           . 
                         
                         
                           6 
                            
                           n 
                         
                       
                     
                     - 
                     
                       
                         λ 
                         
                           1 
                            
                           n 
                         
                       
                        
                       sin 
                        
                       
                           
                       
                        
                       
                         η 
                         n 
                       
                     
                     - 
                     
                       
                         λ 
                         
                           2 
                            
                           n 
                         
                       
                        
                       cos 
                        
                       
                           
                       
                        
                       
                         η 
                         n 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5.109 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         m 
                         sn 
                       
                        
                       
                         { 
                         
                           
                             
                               z 
                               ¨ 
                             
                             
                               6 
                                
                               n 
                             
                           
                           + 
                           
                             
                               α 
                               ¨ 
                             
                              
                             
                               E 
                               2 
                             
                           
                           - 
                           
                             
                               β 
                               ¨ 
                             
                              
                             
                               a 
                               
                                 1 
                                  
                                 n 
                               
                             
                              
                             
                               C 
                               
                                 αγη 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                           
                           - 
                           
                             
                               
                                 η 
                                 . 
                               
                               n 
                               2 
                             
                              
                             
                               z 
                               
                                 6 
                                  
                                 n 
                               
                             
                           
                           - 
                           
                             
                               
                                 α 
                                 . 
                               
                               2 
                             
                              
                             
                               ( 
                               
                                 
                                   z 
                                   
                                     6 
                                      
                                     n 
                                   
                                 
                                 + 
                                 
                                   E 
                                   1 
                                 
                               
                               ) 
                             
                           
                           - 
                           
                             
                               
                                 β 
                                 . 
                               
                               2 
                             
                              
                             
                               B 
                               1 
                             
                              
                             
                               C 
                               
                                 αγη 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                           
                           - 
                           
                             2 
                              
                             
                               
                                 η 
                                 . 
                               
                               n 
                             
                              
                             
                               α 
                               . 
                             
                              
                             
                               z 
                               
                                 6 
                                  
                                 n 
                               
                             
                           
                           + 
                           
                             
                               gC 
                               
                                 αγη 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                              
                             
                               C 
                               β 
                             
                           
                         
                         } 
                       
                     
                     + 
                     
                       
                         k 
                         sn 
                       
                        
                       
                         ( 
                         
                           
                             z 
                             
                               
                                 6 
                                  
                                 n 
                               
                                
                               
                                   
                               
                             
                           
                           - 
                           
                             l 
                             sn 
                           
                         
                         ) 
                       
                     
                   
                   = 
                   
                     
                       
                         - 
                         
                           c 
                           sn 
                         
                       
                        
                       
                         
                           z 
                           . 
                         
                         
                           6 
                            
                           n 
                         
                       
                     
                     - 
                     
                       
                         λ 
                         
                           1 
                            
                           n 
                         
                       
                        
                       
                         S 
                         
                           η 
                            
                           
                               
                           
                            
                           n 
                         
                       
                     
                     - 
                     
                       
                         λ 
                         
                           2 
                            
                           n 
                         
                       
                        
                       
                         C 
                         
                           η 
                            
                           
                               
                           
                            
                           n 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5.110 
                   ) 
                 
               
             
             
               
                 ∴ 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     λ 
                     
                       2 
                        
                       n 
                     
                   
                   = 
                   
                     
                       
                         
                           m 
                           sn 
                         
                          
                         
                           { 
                           
                             
                               
                                 z 
                                 ¨ 
                               
                               
                                 6 
                                  
                                 n 
                               
                             
                             + 
                             
                               
                                 α 
                                 ¨ 
                               
                                
                               
                                 E 
                                 2 
                               
                             
                             - 
                             
                               
                                 β 
                                 ¨ 
                               
                                
                               
                                 a 
                                 
                                   1 
                                    
                                   n 
                                 
                               
                                
                               
                                 C 
                                 
                                   αγη 
                                    
                                   
                                       
                                   
                                    
                                   n 
                                 
                               
                             
                             - 
                             
                               
                                 
                                   η 
                                   . 
                                 
                                 n 
                                 2 
                               
                                
                               
                                 z 
                                 
                                   6 
                                    
                                   n 
                                 
                               
                             
                             - 
                             
                               
                                 
                                   α 
                                   . 
                                 
                                 2 
                               
                                
                               
                                 ( 
                                 
                                   
                                     z 
                                     
                                       6 
                                        
                                       n 
                                     
                                   
                                   + 
                                   
                                     E 
                                     1 
                                   
                                 
                                 ) 
                               
                             
                             - 
                             
                               
                                 
                                   β 
                                   . 
                                 
                                 2 
                               
                                
                               
                                 B 
                                 1 
                               
                                
                               
                                 C 
                                 αγη2 
                               
                             
                             - 
                             
                               
 
                             
                              
                             
                                 
                             
                              
                             
                               2 
                                
                               
                                 
                                   η 
                                   . 
                                 
                                 n 
                               
                                
                               
                                 α 
                                 . 
                               
                                
                               
                                 z 
                                 
                                   6 
                                    
                                   n 
                                 
                               
                             
                             + 
                             
                               g 
                                
                               
                                   
                               
                                
                               
                                 C 
                                 
                                   αγη 
                                    
                                   
                                       
                                   
                                    
                                   n 
                                 
                               
                                
                               
                                 C 
                                 β 
                               
                             
                           
                           } 
                         
                       
                       + 
                       
                         
                           k 
                           sn 
                         
                          
                         
                           ( 
                           
                             
                               z 
                               
                                 6 
                                  
                                 n 
                               
                             
                             - 
                             
                               l 
                               sn 
                             
                           
                           ) 
                         
                       
                       + 
                       
                         
                           c 
                           sn 
                         
                          
                         
                           
                             z 
                             . 
                           
                           
                             
                               6 
                                
                               n 
                             
                              
                             
                                 
                             
                           
                         
                       
                       + 
                       
                         
                           λ 
                           
                             1 
                              
                             n 
                           
                         
                          
                         
                           S 
                           
                             η 
                              
                             
                                 
                             
                              
                             n 
                           
                         
                       
                     
                     
                       - 
                       
                         C 
                         
                           η 
                            
                           
                               
                           
                            
                           n 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5.111 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                            
                           
                              
                             t 
                           
                         
                          
                         
                           ( 
                           
                             
                               ∂ 
                               L 
                             
                             
                               ∂ 
                               
                                 
                                   z 
                                   . 
                                 
                                 
                                   12 
                                    
                                   n 
                                 
                               
                             
                           
                           ) 
                         
                       
                       - 
                       
                         
                           ∂ 
                           L 
                         
                         
                           ∂ 
                           
                             z 
                             
                               12 
                                
                               n 
                             
                           
                         
                       
                     
                     = 
                     
                       
                         
                           
                             ∂ 
                             F 
                           
                           
                             ∂ 
                             
                               
                                 z 
                                 . 
                               
                               
                                 12 
                                  
                                 n 
                               
                             
                           
                         
                         + 
                         
                           
                             ∑ 
                             
                               l 
                               , 
                               n 
                             
                           
                            
                           
                             
                               λ 
                               
                                 l 
                                  
                                 
                                     
                                 
                                  
                                 n 
                               
                             
                              
                             
                               a 
                               
                                 l 
                                  
                                 
                                     
                                 
                                  
                                 n 
                                  
                                 
                                     
                                 
                                  
                                 6 
                               
                             
                              
                             
                                 
                             
                              
                             l 
                           
                         
                       
                       = 
                       1 
                     
                   
                   , 
                   2 
                   , 
                   
                     
                       3 
                        
                       
                           
                       
                        
                       n 
                     
                     = 
                     i 
                   
                   , 
                   ii 
                   , 
                   iii 
                   , 
                   iv 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             k 
                             wn 
                           
                            
                           
                             ( 
                             
                               
                                 z 
                                 
                                   12 
                                    
                                   n 
                                 
                               
                               - 
                               
                                 l 
                                 wn 
                               
                             
                             ) 
                           
                         
                         = 
                         
                             
                         
                          
                         
                           
                             
                               - 
                               
                                 c 
                                 wn 
                               
                             
                              
                             
                               
                                 z 
                                 . 
                               
                               
                                 12 
                                  
                                 n 
                               
                             
                           
                           + 
                           
                             
                               λ 
                               
                                 3 
                                  
                                 n 
                               
                             
                              
                             cos 
                              
                             
                                 
                             
                              
                             α 
                              
                             
                                 
                             
                              
                             cos 
                              
                             
                                 
                             
                              
                             β 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                             
                         
                          
                         
                           
                             
                               - 
                               
                                 c 
                                 wn 
                               
                             
                              
                             
                               
                                 z 
                                 . 
                               
                               
                                 12 
                                  
                                 n 
                               
                             
                           
                           + 
                           
                             
                               λ 
                               
                                 3 
                                  
                                 n 
                               
                             
                              
                             
                               C 
                               α 
                             
                              
                             
                               C 
                               β 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5.112 
                   ) 
                 
               
             
             
               
                 ∴ 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     λ 
                     
                       3 
                        
                       n 
                     
                   
                   = 
                   
                     
                       
                         
                           c 
                           wn 
                         
                          
                         
                           
                             z 
                             . 
                           
                           
                             12 
                              
                             n 
                           
                         
                       
                       + 
                       
                         
                           k 
                           wn 
                         
                          
                         
                           ( 
                           
                             
                               z 
                               
                                 12 
                                  
                                 n 
                               
                             
                             - 
                             
                               l 
                               wn 
                             
                           
                           ) 
                         
                       
                     
                     
                       C 
                       α 
                     
                   
                 
               
               
                 
                   ( 
                   5.113 
                   ) 
                 
               
             
           
         
         
         
             
         
       
     
     From the differentiated constraints it follows that: 
     
       
         {umlaut over (θ)} n   e   2n   S   θn +{dot over (θ)} 
       
     
     
       
         
           n 
           2 
           e 
           2n 
           C 
           θn 
           −{umlaut over (z)} 
         
       
     
     
       
           6n   S   ηn   −{dot over (z)}   6n {dot over (η)} 
       
     
     
       
           n   C   ηn −{umlaut over (η)} n   
       
     
     
       
         ( z   6n   −d   1n ) C   ηn   
       
     
     
       
         −{dot over (η)} n   {dot over (z)}   6n   C   ηn   
       
     
     
       
         +{dot over (η)} n   2   
       
     
     
       
         ( z   6n   −d   1n ) S   ηn =0  
       
     
     
       
         {umlaut over (θ)} n   e   2n   C   θn   
       
     
     
       
         −{dot over (θ)} n   2   e   2n   S   θn   
       
     
     
       
         −{umlaut over (z)} 6n   C   ηn   −{dot over (z)}   6n   
       
     
     
       
         {dot over (η)} n   S   ηn   
       
     
     
       
         −{umlaut over (η)} n ( z   6n   −d   1n )  
       
     
     
       
           S   ηn −{dot over (η)} n   {dot over (z)}   
       
     
     
       
           6n   S   ηn +{dot over (η)} n   2   
       
     
     
       
         ( z   6n   −d   1n ) C   ηn =0 
       
     
     
       
         
           
             
               
                 ∴ 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       η 
                       ¨ 
                     
                     n 
                   
                   = 
                   
                     
                       
                         
                           
                             θ 
                             ¨ 
                           
                           n 
                         
                          
                         
                           e 
                           
                             2 
                              
                             n 
                           
                         
                          
                         
                           S 
                           
                             θ 
                              
                             
                                 
                             
                              
                             n 
                           
                         
                       
                       + 
                       
                         
                           
                             θ 
                             . 
                           
                           n 
                           2 
                         
                          
                         
                           e 
                           
                             2 
                              
                             n 
                           
                         
                          
                         
                           C 
                           
                             θ 
                              
                             
                                 
                             
                              
                             n 
                           
                         
                       
                       - 
                       
                         
                           
                             z 
                             ¨ 
                           
                           
                             6 
                              
                             n 
                           
                         
                          
                         
                           S 
                           
                             η 
                              
                             
                                 
                             
                              
                             n 
                           
                         
                       
                       - 
                       
                         2 
                          
                         
                           
                             η 
                             . 
                           
                           n 
                         
                          
                         
                           
                             z 
                             . 
                           
                           
                             6 
                              
                             n 
                           
                         
                          
                         
                           C 
                           
                             η 
                              
                             
                                 
                             
                              
                             n 
                           
                         
                       
                       + 
                       
                         
 
                       
                        
                       
                           
                       
                        
                       
                         
                           
                             
                               η 
                               . 
                             
                             n 
                             2 
                           
                            
                           
                             ( 
                             
                               
                                 z 
                                 
                                   6 
                                    
                                   n 
                                 
                               
                               - 
                               
                                 d 
                                 
                                   1 
                                    
                                   n 
                                 
                               
                             
                             ) 
                           
                         
                          
                         
                           S 
                           
                             η 
                              
                             
                                 
                             
                              
                             n 
                           
                         
                       
                     
                     
                       
                         ( 
                         
                           
                             z 
                             
                               6 
                                
                               n 
                             
                           
                           - 
                           
                             d 
                             
                               1 
                                
                               n 
                             
                           
                         
                         ) 
                       
                        
                       
                         C 
                         
                           η 
                            
                           
                               
                           
                            
                           n 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5.115 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         z 
                         ¨ 
                       
                       
                         6 
                          
                         n 
                       
                     
                     = 
                     
                       
                         
                           
                             
                               θ 
                               ¨ 
                             
                             n 
                           
                            
                           
                             e 
                             
                               2 
                                
                               n 
                             
                           
                            
                           
                             C 
                             
                               θ 
                                
                               
                                   
                               
                                
                               n 
                             
                           
                         
                         - 
                         
                           
                             
                               θ 
                               . 
                             
                             n 
                             2 
                           
                            
                           
                             e 
                             
                               2 
                                
                               n 
                             
                           
                            
                           
                             S 
                             
                               θ 
                                
                               
                                   
                               
                                
                               n 
                             
                           
                         
                         + 
                         
                           
                             
                               
                                 η 
                                 ¨ 
                               
                               n 
                             
                              
                             
                               ( 
                               
                                 
                                   z 
                                   
                                     6 
                                      
                                     n 
                                   
                                 
                                 - 
                                 
                                   d 
                                   
                                     1 
                                      
                                     n 
                                   
                                 
                               
                               ) 
                             
                           
                            
                           
                             S 
                             
                               η 
                                
                               
                                   
                               
                                
                               n 
                             
                           
                         
                         + 
                         
                           
 
                         
                          
                         
                             
                         
                          
                         
                           2 
                            
                           
                             
                               η 
                               . 
                             
                             n 
                           
                            
                           
                             
                               z 
                               . 
                             
                             
                               6 
                                
                               n 
                             
                           
                            
                           
                             S 
                             
                               η 
                                
                               
                                   
                               
                                
                               n 
                             
                           
                         
                         + 
                         
                           
                             
                               
                                 η 
                                 . 
                               
                               n 
                               2 
                             
                              
                             
                               ( 
                               
                                 
                                   z 
                                   
                                     6 
                                      
                                     n 
                                   
                                 
                                 - 
                                 
                                   d 
                                   
                                     1 
                                      
                                     n 
                                   
                                 
                               
                               ) 
                             
                           
                            
                           
                             C 
                             
                               η 
                                
                               
                                   
                               
                                
                               n 
                             
                           
                         
                       
                       
                         C 
                         
                           η 
                            
                           
                               
                           
                            
                           n 
                         
                       
                     
                   
                    
                   
                       
                   
                 
               
               
                 
                   ( 
                   5.116 
                   ) 
                 
               
             
             
               
                 and 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       z 
                       . 
                     
                     
                       12 
                        
                       n 
                     
                   
                   = 
                   
                     
                       
                         
                           { 
                           
                             
                               
                                 α 
                                 . 
                               
                                
                               
                                 z 
                                 
                                   12 
                                    
                                   n 
                                 
                               
                                
                               
                                 S 
                                 α 
                               
                             
                             - 
                             
                               
                                 ( 
                                 
                                   
                                     α 
                                     . 
                                   
                                   + 
                                   
                                     
                                       θ 
                                       . 
                                     
                                     n 
                                   
                                 
                                 ) 
                               
                                
                               
                                 e 
                                 
                                   3 
                                    
                                   n 
                                 
                               
                                
                               
                                 C 
                                 
                                   αγθ 
                                    
                                   
                                       
                                   
                                    
                                   n 
                                 
                               
                             
                             + 
                             
                               
                                 α 
                                 . 
                               
                                
                               
                                 c 
                                 
                                   2 
                                    
                                   n 
                                 
                               
                                
                               
                                 S 
                                 
                                   αγ 
                                    
                                   
                                       
                                   
                                    
                                   n 
                                 
                               
                             
                             - 
                             
                               
 
                             
                              
                             
                               
                                 α 
                                 . 
                               
                                
                               
                                 b 
                                 
                                   2 
                                    
                                   n 
                                 
                               
                                
                               
                                 C 
                                 a 
                               
                             
                           
                           } 
                         
                          
                         
                           C 
                           β 
                         
                       
                       - 
                       
                         
                           z 
                           . 
                         
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                   ( 
                   5.117 
                   ) 
                 
               
             
           
         
         
         
             
         
       
     
     Supplemental differentiation of equation (5.113) for the later entropy production calculation yields: 
     
       
           k   wn   {dot over (z)}   12n   =−c   wn   {umlaut over (z)}   12n +{dot over (λ)} 3n   C   α   C   β −{dot over (α)}λ 3n   S   α   C   62  −{dot over (β)}λ 3n   C   α   S   62    (5.118) 
       
     
     therefore                  z   ¨       12      n       =             λ   .       3      n            C   α          C     β                    -       α   .          λ     3      n            S   α          C   β       -       β   .          λ     3      n            C   α          S   β       -       k   wn            z   .       12      n             c   wn               (   5.119   )                         
      or from the third equation of constraint:                    z   ¨     0     +       {           z   ¨         12      n                       cos                 α     -         z   .       12      n            α   .        cos                 α     -       α   ¨          z     12      n          sin                 α     -       α   .            z   .       12      n          sin                 α     -         α   .     2          z     12                 n          cos                 α     +       (       α   ¨     +       θ   .     n       )          e       3      n                         cos        (     α   +     γ   n     +     θ   n       )         -         (       α   .     +       θ   .     n       )     2          e     3      n            sin        (     α   +     γ   n     +     θ   n       )         -       α   ¨          c     2      n            sin        (     α   +     γ   n       )         -         α   .       2                       c     2      n            cos        (     α   +     γ   n       )         +       α   ¨          b     2      n          cos                 α     -         α   .     2          b     2      n          sin                 α       }        cos                 β     -       β   .          {           z   .       12      n          cos                 α     -       α   .          z     12      n          sin                 α     +       (       α   .     +       θ   .     n       )          e     3      n            cos        (     α   +     γ   n     +     θ   n       )         -       α   .          c     2      n            sin        (     α   +     γ   n       )         +       α   .          b     2      n          cos                 α       }        sin                 β     -       β   ¨          [         {         z     12      n          cos                 α     +       e     3      n            sin        (     α   +     γ   n     +     θ   n       )         +       c     2      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }        sin                 β     +       a     1      n          cos                 β       ]       -       β   .          [         {           z   .       12      n          cos                 α     -       α   .          z     12      n          sin                 α     +       (       α   .     +       θ   .     n       )          e     3      n            cos        (     α   +     γ   n     +     θ   n       )         -       (       α   .     +       γ   .     n       )          c     2      n            sin        (     α   +     γ   n       )         +       α   .          b       2      n                       cos                 α       }        sin                 β     +       β   .          {         z     12      n          cos                 α     +       e     3      n            sin        (     α   +     γ   n     +     θ   n       )         +       c     2      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }        cos                 β     -       β   .          a     1      n          sin                 β       ]       -         R   ¨     n          (   t   )         =   0           (   5.120   )                   z   ¨       12      n       =                          z   ¨     0     +       {         -       z   .       12      n              α   .        cos                 α     -       α   ¨          z       12      n                       sin                 α     -       α   .            z   .       12      n          sin                 α     -     
                         α   .     2          z     12      n          cos                 α     +       (       α   ¨     +       θ   .     n       )          e     3      n            cos        (     α   +     γ   n     +     θ   n       )         -                    (       α   .     +       θ   .     n       )     2          e     3      n            sin        (     α   +     γ   n     +     θ   n       )         -     
                       α   ¨          c     2      n            sin        (     α   +     γ   n       )         -         α   .     2          c     2      n            cos        (     α   +     γ   n       )         +     
                       α   ¨          b     2      n          cos                 α     -         α   .     2          b     2      n          sin                 α       }        cos                 β     -       β   .          {                 z   .       12      n          cos                 α     -     
                       α   .          z     12      n          sin                 α     +       (       α   .     +       θ   .     n       )          e     3      n            cos        (     α   +     γ   n     +     θ   n       )         -     
                       α   .          c     2      n            sin        (     α   +     γ   n       )         +       α   .          b     2      n          cos                 α       }        sin                 β     -       β   ¨          [         {         z     12      n          cos                 α     +     
            e     3      n            sin        (     α   +     γ   n     +     θ   n       )         +       c       2      n                         cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }        sin                 β     +     
                       a     1      n          cos                 β       ]       -       β   .          [         {           z   .       12      n          cos                 α     -       α   .          z     12      n          sin                 α     +     
            (       α   .     +       θ   .     n       )          e     3      n            cos        (     α   +     γ   n     +     θ   n       )         -       (       α   .     +       γ   .     n       )          c     2      n            sin        (     α   +     γ   n       )         +     
                       α   .          b     2      n          cos                 α       }        sin                 β     +       β   .          {         z     12      n          cos                 α     +       e     3      n            sin        (     α   +     γ   n     +     θ   n       )         +     
                       c     2      n            cos        (     α   +     γ   n       )         +       b     2      n          sin                 α       }        cos                 β     -       β   .          a     1      n          sin                 β       ]       -         R   ¨     n          (   t   )                                  -   cos                   α                 cos                 β               (   5.121   )                         
     Equations for entropy production are developed below. Minimum entropy production (for use in the fitness function of the genetic algorithm) is expressed as:                       β        S          t       =               -   2                         β   .     2     [         α   .                     m   b          A   1          A   2       +       m   sn          B   1          {           z   .       6      n            C     α                 γ                 η                 n         -       (       α   .     +       η   .     n       )          z     6      n            S     α                 γ                 η                 n         -                               α   .          A   4       }     +       m   an          B   2          {         (       α   .     +       θ   .     n       )          e     1      n            C     α                 γ                 θ                 n         -       α   .          A   6         }       +       m   wn          B   3          {     (       α   .     +                                     θ   .     n     )          e     3      n            S     α                 γ                 θ                 n         -       α   .          A   6         }     -           z   .     0          (       m   ba     +     m   sawan       )              S   β     /   2         ]               m   saw2n     +     m   baI     +       m   b          A   1   2       +       m   sn          B   1   2       +       m   an          B   2   2       +       m   wn          B   3   2                   (   5.122   )                        α        S          t       =         -   2            α   .     2          {         m   sn          α   .              z   .       6      n            (       z     6      n       +     E     1      n         )         +       m   sn          z     6      n              η   .     n          E     2      n         +         θ   .     n          m   aw1n          H     2      n           }           m   bbI     +     m   sawIn     +       m   sn            z     6      n            (       z     6      n       +     2        E     1      n           )         -     2        m   aw1n          H     1      n                     (   5.123   )                          η   n          S          t       =           η   .     n   3        tg                   η   n       -       2                     η   .     n   2            z   .       6      n             z     6      n       -     d     1      n                     (   5.124   )                          z     6      n            S          t       =     2                     η   .     n            z   .       6      n     2        tg                   η   n               (   5.125   )                          z     12      n            S          t       =         z   .       12      n     2          (       α   .     +       α   .                   tg                 α     +     2                   β   .                   tg                 β       )               (   5.126   )                         
     FIG. 8A shows the vehicle body  710  and the wheels  702  and  704  (the wheels  701  and  703  are hidden). FIG. 8A also shows dampers  801 - 804  configured to provide adjustable damping for the wheels  701 - 704  respectively. In one embodiment, the dampers  801 - 804  are electronically-controlled dampers. In one embodiment, a stepping motor actuator on each damper controls an oil valve. Oil flow in each rotary valve position determines the damping factor provided by the damper. 
     FIG. 8B shows an adjustable damper  817  having an actuator  818  that controls a rotary valve  812 . A hard-damping valve  811  allows fluid to in the adjustable damper  817  to produce hard damping. A soft-damping valve  813  allows fluid to flow in the adjustable damper  817  to produce soft damping. The rotary valve  812  controls the amount of fluid that flows through the soft-damping valve  813 . The actuator  818  controls the rotary valve  812  to allow more or less fluid to flow through the soft-damping valve  813 , thereby producing a desired damping. In one embodiment, the actuator  818  is a stepping motor. The actuator  818  receives control signals from the controller  810 . 
     FIG. 8C shows fluid flow through the soft-damping valve  813  when the rotary valve  812  is opened. FIG. 8C also shows fluid flow through the hard-damping valve  810  when then rotary valve  812  is closed. 
     FIG. 9 shows damper force characteristics as damper force versus piston speed characteristics when the rotary valve is placed in a hard damping position and in a soft damping position. The valve is controlled by the stepping motor to be placed between the soft and the hard damping positions to generate intermediate damping force. 
     The SSCQ  130 , shown in FIG. 2, is an off-line block that produces the teaching signal K i  for the FLCS  140 . FIG. 10 shows the structure of an SSCQ  1030  for use in connection with a simulation model of the full car and suspension system. The SSCQ  1030  is one embodiment of the SSCQ  130 . In addition to the SSCQ  1030 , FIG. 10 also shows a stochastic road signal generator  1010 , a suspension system simulation model  1020 , a proportional damping force controller  1050 , and a timer  1021 . The SSCQ  1030  includes a mode selector  1029 , an output buffer  1001 , a GA  1031 , a buffer  1022 , a proportional damping force controller  1034 , a fitness function calculator  1032 , and an evaluation model  1036 . 
     The Timer  1021  controls the activation moments of the SSCQ  1030 . An output of the timer  1021  is provided to an input of the mode selector  1029 . The mode selector  1029  controls operational modes of the SSCQ  1030 . In the SSCQ  1030 , a reference signal y is provided to a first input of the fitness function calculator  1032 . An output of the fitness function calculator  1032  is provided to an input of the GA  1031 . A CGS e  output of the GA  1031  is provided to a training input of the damping force controller  1034  through the buffer  1022 . An output of the damping force controller  1034  is provided to an input of the evaluation model  1036 . An X e  output of the evaluation model  1036  is provided to a second input of the fitness function calculator  1032 . A CGS i  output of the GA  1031  is provided (through the buffer  1001 ) to a training input of the damping force controller  1050 . A control output from the damping force controller  1050  is provided to a control input of the suspension system simulation model  1020 . The stochastic road signal generator  1010  provides a stochastic road signal to a disturbance input of the suspension system simulation model  1020  and to a disturbance input of the evaluation model  1036 . A response output X i  from the suspension system simulation model  1020  is provided to a training input of the evaluation model  1036 . The output vector K i  from the SSCQ  1030  is obtained by combining the CGS i  output from the GA  1031  (through the buffer  1001 ) and the response signal X i  from the suspension system simulation model  1020 . 
     Road signal generator  1010  generates a road profile. The road profile can be generated from stochastic simulations as described above in connection with FIGS. 4-6F, or the road profile can be generated from measured road data. The road signal generator  1010  generates a road signal for each time instant (e.g., each clock cycle) generated by the timer  1021 . 
     The simulation model  1020  is a kinetic model of the full car and suspension system with equations of motion, as obtained, for example, in connection with FIG.  7 . In one embodiment, the simulation model  1020  is integrated using high-precision order differential equation solvers. 
     The SSCQ  1030  is an optimization module that operates on a discrete time basis. In one embodiment, the sampling time of the SSCQ  1030  is the same as the sampling time of the control system  1050 . Entropy production rate is calculated by the evaluation model  1036 , and the entropy values are included into the output (X e ) of the evaluation model  1036 . 
     The following designations regarding time moments are used herein: 
     T=Moments of SSCQ calls 
     T c =the sampling time of the control system  1050   
     T e =the evaluation (observation) time of the SSCQ  1030   
     t c =the integration interval of the simulation model  1004  with fixed control parameters, t c ∈[T;T+T c ] 
     t e =Evaluation (Observation) time interval of the SSCQ, te∈[T;T+Te] 
     FIG. 11 is a flowchart showing operation of the SSCQ  1030  as follows: 
     1. At the initial moment (T=0) the SSCQ  1030  is activated and the SSCQ  1030  generates the initial control signal CGS i (T). 
     2. The simulation model  1020  is integrated using the road signal from the stochastic road generator  1010  and the control signal CGS i (T) on a first time interval t c  to generate the output X i . 
     3. The output X i  and with the output CGS i (T) are is saved into the data file  1060  as a teaching signal K i . 
     4. The time interval T is incremented by T c (T=T+T c ). 
     5. The sequence 1-4 is repeated a desired number of times (that is while T&lt;T F ). In one embodiment, the sequence 1-4 is repeated until the end of road signal is reached 
     Regarding step 1 above, the SSCQ block has two operating modes: 
     1. Updating of the buffer  1001  using the GA  1031   
     2. Extraction of the output CGS i (T) from the buffer  1001 . 
     The operating mode of the SSCQ  1030  is controlled by the mode selector  1029  using information regarding the current time moment T, as shown in FIG.  12 . At intervals of T e  the SSCQ  1030  updates the output buffer  1001  with results from the GA  1031 . During the interval T e  at each interval T c , the SSCQ extracts the vector CGS i  from the output buffer  1001 . 
     FIG. 13 is a flowchart  1300  showing operation of the SSCQ  1030  in connection with the GA  1031  to compute the control signal CGS i . The flowchart  1300  begins at a decision block  1301 , where the operating mode of the SSCQ  1030  is determined. If the operating mode is a GA mode, then the process advances to a step  1302 ; otherwise, the process advances to a step  1310 . In the step  1302 , the GA  1031  is initialized, the evaluation model  1036  is initialized, the output buffer  1001  is cleared, and the process advances to a step  1303 . In the step  1303 , the GA  1031  is started, and the process advances to a step  1304  where an initial population of chromosomes is generated. The process then advances to a step  1305  where a fitness value is assigned to each chromosome. The process of assigning a fitness value to each chromosome is shown in an evaluation function calculation, shown as a sub-flowchart having steps  1322 - 1325 . In the step  1322 , the current states of X i (T) are initialized as initial states of the evaluation model  1036 , and the current chromosome is decoded and stored in the evaluation buffer  1022 . The sub-process then advances to the step  1323 . The step  1323  is provided to integrate the evaluation model  1036  on time interval t e  using the road signal from the road generator  1010  and the control signal CGS e (t e ) from the evaluation buffer  1022 . The process then advances to the step  1324  where a fitness value is calculated by the fitness function calculator  1032  by using the output X e  from the evaluation model  1036 . The output X e  is a response from the evaluation model  1036  to the control signals CGS e (t e ) which are coded into the current chromosome. The process then advances to the step  1325  where the fitness value is returned to the step  1305 . After the step  1305 , the process advances to a decision block  1306  to test for termination of the GA. If the GA is not to be terminated, then the process advances to a step  1307  where a new generation of chromosomes is generated, and the process then returns to the step  1305  to evaluate the new generation. If the GA is to be terminated, then the process advances to the step  1309 , where the best chromosome of the final generation of the GA, is decoded and stored in the output buffer  1001 . After storing the decoded chromosome, the process advances to the step  1310  where the current control value CGS i (T) is extracted from the output buffer  1001 . 
     The structure of the output buffer  1001  is shown below as a set of row vectors, where first element of each row is a time value, and the other elements of each row are the control parameters associated with these time values. The values for each row include a damper valve position VP FL , VP FR , VP RL , VP RR , corresponding to front-left, front-right, rear-left, and rear-right respectively. 
     
       
         
           
               
               
             
               
                   
               
               
                 Time* 
                 CGS i   
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 T 
                 VP FL (T)** 
                 VP FR (T) 
                 VP RL (T) 
                 VP RR (T) 
               
               
                 T + T c   
                 VP FL (T + T c ) 
                 VP FR (T + T c ) 
                 VP RL (T + T c ) 
                 VP RR (T + T c ) 
               
               
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
               
               
                 T + T e   
                 VP FL (T + T e ) 
                 VP FR (T + T e ) 
                 VP RL (T + T e ) 
                 VP RR (T + T e ) 
               
               
                   
               
            
           
         
       
     
     The output buffer  1001  stores optimal control values for evaluation time interval t e  from the control simulation model, and the evaluation buffer  1022  stores temporal control values for evaluation on the interval t e  for calculation of the fitness function. 
     Two simulation models are used. The simulation model  1020  is used for simulation and the evaluation model  1036  is used for evaluation. There are many different methods for numerical integration of systems of differential equations. Practically, these methods can be classified into two main classes: (1) variable-step integration methods with control of integration error; and (2) fixed-step integration methods without integration error control. 
     Numerical integration using methods of type (1) is very precise, but time-consuming. Methods of type (2) are typically faster, but with smaller precision. During each SSCQ call in the GA mode, the GA  1031  evaluates the fitness function  1032  many times and each fitness function calculation requires integration of the model of dynamic system (the integration is done each time). By choosing a small-enough integration step size, it is possible to adjust a fixed-step solver such that the integration error on a relatively small time interval (like the evaluation interval t e ) will be small and it is possible to use the fixed-step integration in the evaluation loop for integration of the evaluation model  1036 . In order to reduce total integration error it is possible to use the result of high-order variable-step integration of the simulation model  1020  as initial conditions for evaluation model integration. The use of variable-step solvers to integrate the evaluation model can provide better numerical precision, but at the expense of greater computational overhead and thus longer run times, especially for complicated models. 
     The fitness function calculation block  1032  computes a fitness function using the reference signal Y and the response (X e ) from the evaluation model  1036  (due to the control signal CGS e (t e ) provided to the evaluation module  1036 ). 
     The fitness function  1032  is computed as a vector of selected components of a matrix (x e ) and its squared absolute value using the following form:                  Fitness   2     =         ∑     t   ∈     [     T   ;     T   e       ]              [         ∑   i              w   i     (     x   it   e     )     2       +       ∑   j              w   j     (       y   j     -     x   jt   e       )     2       +       ∑   k            w   k            f   (     x   kt   e     )     2           ]       →   min       ,           (   6.1   )                         
     where: 
     i denotes indexes of state variables which should be minimized by their absolute value; j denotes indexes of state variables whose control error should be minimized; k denotes indexes of state variables whose frequency components should be minimized; and w r , r=i,j,k are weighting factors which represent the importance of the corresponding parameter from the human feelings point of view. By setting these weighting function parameters, it is possible to emphasize those elements from the output of the evaluation model that are correlated with the desired human requirements (e.g., handling, ride quality, etc.). In one embodiment, the weighting factors are initialized using empirical values and then the weighting factors are adjusted using experimental results. 
     Extraction of frequency components can be done using standard digital filtering design techniques for obtaining the filter parameters. Digital filtering can be provided by a standard difference equation applied to elements of the matrix X e :                        a        (   1   )            f        (       x   k   e          (       t   e          (   N   )       )       )         =                    b        (   1   )              x   k   e          (       t   e          (   N   )       )         +       b        (   2   )              x   k   e          (       t   e          (     N   -   1     )       )         +   …   +                                  b        (       n   b     +   1     )              x   k   e          (       t   e          (     N   -     n   b       )       )         -                                  -   a          (   2   )            x   k   e          (       t   e          (     N   -   1     )       )         -   …   -                  a        (       n   a     +   1     )              x   k   e          (       t   e          (     N   -     n   a       )       )                         (   6.2   )                         
     where a,b are parameters of the filter, N is the number of the current point, and n b ,n a  describe the order of the filter. In case of a Butterworth filter, n b =n a . 
     In one embodiment, the GA  1031  is a global search algorithms based on the mechanics of natural genetics and natural selection. In the genetic search, each a design variable is represented by a finite length binary string and then these finite binary strings are connected in a head-to-tail manner to form a single binary string. Possible solutions are coded or represented by a population of binary strings. Genetic transformations analogous to biological reproduction and evolution are subsequently used to improve and vary the coded solutions. Usually, three principle operators, i.e., reproduction (selection), crossover, and mutation are used in the genetic search. 
     The reproduction process biases the search toward producing more fit members in the population and eliminating the less fit ones. Hence, a fitness value is first assigned to each string (chromosome) the population. One simple approach to select members from an initial population to participate in the reproduction is to assign each member a probability of selection on the basis of its fitness value. A new population pool of the same size as the original is then created with a higher average fitness value. 
     The process of reproduction simply results in more copies of the dominant or fit designs to be present in the population. The crossover process allows for an exchange of design characteristics among members of the population pool with the intent of improving the fitness of the next generation. Crossover is executed by selecting strings of two mating parents, randomly choosing two sites. 
     Mutation safeguards the genetic search process from a premature loss of valuable genetic material during reproduction and crossover. The process of mutation is simply to choose few members from the population pool according to the probability of mutation and to switch a 0 to 1 or vice versa at randomly sites on the chromosome. 
     FIG. 14 illustrates the processes of reproduction, crossover and mutation on a set of chromosomes in a genetic analyzer. A population of strings is first transformed into decimal codes and then sent into the physical process  1407  for computing the fitness of the strings in the population. A biased roulette wheel  1402 , where each string has a roulette wheel slot sized in proportion to its fitness is created. A spinning of the weighted roulette wheel yields the reproduction candidate. In this way, a higher fitness of strings has a higher number of offspring in the succeeding generation. Once a string has been selected for reproduction, a replica of the string based on its fitness is created and then entered into a mating pool  1401  for waiting the further genetic operations. After reproduction, a new population of strings is generated through the evolutionary processes of crossover  1404  and mutation  1405  to produce a new parent population  1406 . Finally, the whole genetic process, as mentioned above, is repeated again and again until an optimal solution is found. 
     The Fuzzy Logic Control System (FLCS)  240  shown in FIG. 2 includes the information filter  241 , the FNN  142  and the FC  143 . The information filter  241  compresses the teaching signal K i  to obtain the simplified teaching signal K c , which is used with the FNN  142 . The FNN  142 , by interpolation of the simplified teaching signal K c , obtains the knowledge base (KB) for the FC  143 . 
     As it was described above, the output of the SSCQ is a teaching signal K i  that contains the information of the behavior of the controller and the reaction of the controlled object to that control. Genetic algorithms in general perform a stochastic search. The output of such a search typically contains much unnecessary information (e.g., stochastic noise), and as a result such a signal can be difficult to interpolate. In order to exclude the unnecessary information from the teaching signal K i , the information filter  241  (using as a background the Shannon&#39;s information theory) is provided. For example, suppose that A is a message source that produces the message a with probability p(a), and further suppose that it is desired to represent the messages with sequences of binary digits (bits) that are as short as possible. It can be shown that the mean length L of these bit sequences is bounded from below by the Shannon entropy H(A) of the source: L≧H(A), where                H        (   A   )       =     -       ∑   a            p        (   s   )            log   2          p        (   a   )                     (   7.1   )                         
     Furthermore, if entire blocks of independent messages are coded together, then the mean number {overscore (L)} of bits per message can be brought arbitrary close to H(A). 
     This noiseless coding theorem shows the importance of the Shannon entropy H(A) for the information theory. It also provides the interpretation of H(A) as a mean number of bits necessary to code the output of A using an ideal code. Each bit has a fixed ‘cost’ (in units of energy or space or money), so that H(A) is a measure of the tangible resources necessary to represent the information produced by A. 
     In classical statistical mechanics, in fact, the statistical entropy is formally identically to the Shannon entropy. The entropy of a macrostate can be interpreted as the number of bits that would be required to specify the microstate of the system. 
     Suppose x 1 , . . . , x N  are N independent, identical distributed random variables, each with mean {overscore (x)} and finite variance. Given δ, ε&gt;0, there exist N 0  such that, for N≧N 0 ,                P        (     |         1   N            ∑   i          x   i         -     x   _       |     &gt;   δ       )       &lt;   ɛ           (   7.2   )                         
     This result is known as the weak law of large numbers. A sufficiently long sequence of independent, identically distributed random variables will, with a probability approaching unity, have an average that is close to mean of each variable. 
     The weak law can be used to derive a relation between Shannon entropy H(A) and the number of ‘likely’ sequences of N identical random variables. Assume that a message source A produces the message a with probability p(a). A sequence α=a 1 a 2  . . . a N  of N independent messages from the same source will occur in ensemble of all N sequences with probability P(α)=p(a 1 )·p(a 2 ) . . . p(a N ). Now define a random variable for each message by x=−log 2 p(a), so that H(A)={overscore (x)}. It is easy to see that            -     log   2            P        (   α   )         =       ∑   i            x   i     .                       
     From the weak law, it follows that, if ε,δ&gt;0, then for sufficient large N                P        (     |         -     1   N            log   2          P        (   α   )         -     H        (   A   )         |     &gt;   δ       )       &lt;   ɛ           (   7.3   )                         
     for N sequences of α. It is possible to partition the set of all N sequences into two subsets: 
     a) A set Λ of “likely” sequences for which        |         -     1   N            log   2          P        (   α   )         -     H        (   A   )         |     ≤   δ                     
     b) A set of ‘unlikely’ sequences with total probability less than ε, for which this inequality fails. 
     This provides the possibility to exclude the ‘unlikely’ information from the set Λ which leaves the set of sequences Λ 1  with the same information amount as in set Λ but with a smaller number of sequences. 
     The FNN  142  is used to find the relations between (Input) and (Output) components of the teaching signal K c . The FNN  142  is a tool that allows modeling of a system based on a fuzzy logic data structure, starting from the sampling of a process/function expressed in terms of input-output values pairs (patterns). Its primary capability is the automatic generation of a database containing the inference rules and the parameters describing the membership functions. The generated Fuzzy Logic knowledge base (KB) represents an optimized approximation of the process/function provided as input. FNN performs rule extraction and membership function parameter tuning using learning different learning methods, like error back propagation, fuzzy clustering, etc. The KB includes a rule base and a database. The rule base stores the information of each fuzzy rule. The database stores the parameters of the membership functions. Usually, in the training stage of FNN, the parts of KB are obtained separately. 
     An example of a KB of a suspension system fuzzy controller obtained using the FNN  142  is presented in FIG.  15 . The knowledge base of a fuzzy controller includes two parts, a database where parameters of membership functions are stored, and a database of rules where fuzzy rules are stored. In the example shown in FIG. 15, the fuzzy controller has two inputs (ANT 1 ) and (ANT 2 ) which are pitch angle acceleration and roll angle acceleration, and 4 output variables (CONS 1  , . . . CONS 4 ), are the valve positions of FL, FR, RL, RR wheels respectively. Each input variable has 5 membership functions, which gives total number of 25 rules. 
     The type of fuzzy inference system in this case is a zero-order Sugeno-Takagi Fuzzy inference system. In this case the rule base has the form presented in the list below. 
     IF ANT 1  is MBF 1 _ 1  and ANT 2  is MBF 2 _ 1  then CONS 1  is A 1 _ 1  and . . . and CONS 4  is A 4 _ 1   
     IF ANT 1  is MBF 1 _ 1  and ANT 2  is MBF 2 _ 2  then CONS 1  is A 1 _ 2  and . . . and CONS 4  is A 4 _ 2   
     . . . 
     IF ANT 1  is MBF 1 _ 5  and ANT 2  is MBF 25  then CONS 1  is A 1 _ 25  and . . . and CONS 4  is A 4 _ 25   
     In the example above, when there are only 25 possible combinations of input membership functions, so it is possible to use all the possible rules. However, when the number of input variables is large, the phenomenon known as “rule blow” takes place. For example, if number of input variables is 6, and each of them has 5 membership functions, then the total number of rules could be: N=5 6 =15625 rules. In this case practical realization of such a rule base will be almost impossible due to hardware limitations of existing fuzzy controllers. There are different strategies to avoid this problem, such as assigning fitness value to each rule, and exclusion of rules with small fitness from the rule base. The rule base will be incomplete, but realizable. 
     The FC  143  is an on-line device that generates the control signals using the input information from the sensors comprising the following steps: (1) fuzzyfication; (2) fuzzy inference; and (3) defuzzyfication. 
     Fuzzyfication is a transferring of numerical data from sensors into a linguistic plane by assigning membership degree to each membership function. The information of input membership function parameters stored in the knowledge base of fuzzy controller is used. 
     Fuzzy inference is a procedure that generates linguistic output from the set of linguistic inputs obtained after fuzzyfication. In order to perform the fuzzy inference, the information of rules and of output membership functions from knowledge base is used. 
     Defuzzyfication is a process of converting of linguistic information into the digital plane. Usually, the process of defuzzyfication include selecting of center of gravity of a resulted linguistic membership function. 
     Fuzzy control of a suspension system is aimed at coordinating damping factors of each damper to control parameters of motion of car body. Parameters of motion can include, for example, pitching motion, rolling motion, heave movement, and/or derivatives of these parameters. Fuzzy control in this case can be realized in the different ways, and different number of fuzzy controllers used. For example, in one embodiment shown in FIG. 16A, fuzzy control is implemented using two separate controllers, one controller for the front wheels, and one controller for the rear wheels, as shown in FIG. 16A, where a first fuzzy controller  1601  controls front-wheel damper actuators  1603  and  1604  and a second fuzzy controller  1602  controls rear-wheel damper actuators  1605  and  1606 . In one embodiment, shown in FIG. 16B, a single controller  1610  controls the actuators  1603 - 1606 . 
     As described above in connection with Equation 7.3, it is possible to exclude the “unlikely” information from the set Λ, which leaves the set of sequences Λ 1  having approximately the same amount of information as in set Λ, but with a smaller number of sequences. The results of such a filtering algorithm application are illustrated in FIGS. 17 and 18. In the FIG. 17, the filtering is applied to the matrix of normal distribution values. The source signal (shown in curve (a) of FIG. 17) is a data matrix, containing 100 rows and one column of Gaussian-normal distributed values with mean zero and with σ 2 =1. Labels on the X axis denote the row number. The value of ε is chosen as the mean value of the information distribution (as shown in curve (b) of FIG.  17 ). After applying the information filter, the resulting filtered signal has less than 40 percent of the rows of the source signal (as shown in curve (c) of FIG.  17 ). The other rows have little significant information and can be eliminated. The information distribution of the resulting signal is shown in curve (d) of FIG.  17 . The number of “in-out” teaching pairs in the compressed signal K c (N=3587) shown in FIG. 18 is almost two times less than the number of “in-out” teaching pairs in the entire teaching signal K i  (N=7201), shown in FIG.  19 . The form of the teaching signals remains the same, and both teaching signals have approximately the same amount of information. FIGS. 18 and 19 include curves showing speed of the vehicle. 
     FIGS. 18 and 19 also include curves showing acceleration of the front-left portion of the vehicle body  710  (labeled BA_fl in FIGS.  18  and  19 ), acceleration of the front-right portion of the vehicle body  710  (labeled BA_fr in FIGS.  18  and  19 ), acceleration of the rear-left portion of the vehicle body  710  (labeled BA_rl in FIGS.  18  and  19 ), and acceleration of the rear-right portion of the vehicle body  710  (labeled BA_rr in FIGS. 18 and 19) in meters per second squared. FIGS. 18 and 19 also include curves showing vertical velocity of the front-left damper  802  (labeled DV_fl in FIGS.  18  and  19 ), vertical velocity of the front-right damper  801  (labeled DV_fr in FIGS.  18  and  19 ), vertical velocity of the rear-left damper  804  (labeled DV_rl in FIGS.  18  and  19 ), and vertical velocity of the rear-right damper  803  (labeled DV_rr in FIGS. 18 and 19) in meters per second. Finally, FIGS. 18 and 19 include curves showing valve position of the front-left damper  802  (VP_fl), valve position of the front-right damper  801  (VP_fr), valve position of the rear-left damper  804  (VP_rl), and valve position of the rear-right damper  803  (VP_rr). The x-axes of the plots shown in FIGS. 18-19 indicate the sample points. The curves in FIG. 18 correspond to 3587 sample points. The curves in FIG. 19 correspond to 7201 sample points. 
     FIG. 20 shows simulation results of fuzzy control of a suspension system, when a fuzzy logic classifier system, such as the fuzzy logic classifier system  140 , is trained using the entire teaching signal K i  (shown in FIG.  19 ). FIG. 20 also shows simulation results of fuzzy control of the same system when the fuzzy logic classifier system  140  is trained using the filtered teaching signal K c  (shown in FIG.  18 ). In the first case (solid line), the controller was trained using the full teaching signal K i . In the second case (dashed line), the controller was trained with the teaching signal, which was filtered using the information filter  241 . In FIG. 20, heave (Z 0 ), pitch (BT) and roll (AL) movements, velocities and accelerations are shown. FIG. 20 shows the similarity of the system outputs in both cases, indicating the positive result of teaching signal filtering using the information filter  241 . 
     FIGS. 21-23 show experimental results of fuzzy control. For the curves shown in FIGS. 21-23, the fitness function in the genetic algorithm is designed to minimize: 
     
       
         (heave jerk) 2 +(pitch jerk) 2 +(roll jerk) 2 +(entropy production) 2   
       
     
     FIG. 21 shows the squared of the controlled (solid line) and uncontrolled (dashed line) heave jerk. FIG. 22 shows the square of the controlled (solid line) and uncontrolled (dashed line) pitch jerk. FIG. 23 shows the square of the controlled (solid line) and uncontrolled (dashed line) heave jerk. 
     Appendix I: Mathematical and Physical Background of Stochastic Simulation 
     1. Stochastic Integrals and Stochastic Differential Equations 
     1.1. Stochastic Integrals 
     Consider different types of stochastic integral according to increasing complexity:          A   .                  ∫   0   t            Φ        (   τ   )               τ           ;                B   .                  ∫   0   t            Φ   (       y        (   τ   )       ,   τ     )               y        (   τ   )               ;                C   .                  ∫   0   t            Φ   (       x        (   τ   )       ,   τ     )               y        (   τ   )                               
     where y(τ) is the process of Brownian motion [M[y(τ j+1 )−y(τ j )]=0,M[y(τ j+1 )−y(τ j )] 2 =[τ j+1 −τ j ], (if(τ j , τ j+1 )∩(τ k , τ k+1 )=0 then the increments are independent and M[y(τ j+1 )−y(τ j )][y(τ k+1 )−y(τ k )]=0) and x(τ) is a smoothly Markovian process. Define the stochastic integrals of types A, B, and C as limits in mean-square (1.i.m.) of integral sums. 
     Case A: Assume that Φ(τ) is a smooth function and            ∫   0   ∞              Φ   2          (   τ   )               τ         &lt;     ∞   .                     
     In this case: 1.i.m.          ∫   0   t          [           Φ   n          (   τ   )       -       (       Φ        (   τ   )       2     ]             τ         →   0                       
     for n→∞, where Φ n (τ) is the sequence of step functions. Define the integral for a step functions as            S   n     =         ∫   0   t              Φ   n          (   τ   )                 y        (   τ   )             =       ∑     j   =   1     N                         Φ   n          (     τ   j     )            [       y        (     τ     j   +   1       )       -     y        (     τ   j     )         ]             ,                   
     where (τ j ,τ j+1 ) is the step of a function Φ n (τ) (see FIG. I.6). 
     The limit in mean-square for the sequence of random functions S n (t) exists if M[S n −S m ] 2 →0 for n,m→∞. In this case M[S n (t)−S m (t)] 2 =∫[Φ n (τ)−Φ m (τ)] 2 dτ and this integral is similar to the Riemannian integral. 
     Case B: Assume that Φ(y,t) is the differentiable function of both arguments and            ∫   0   t            M        [       Φ   2          (       y        (   τ   )       ,   τ     )       ]               τ         &lt;     ∞   .                     
     The stochastic Ito integral (case B) is:              l   .   i   .   m   .            N   →   ∞                ∑     j   =   1     N                       Φ        (       y        (     τ   j     )       ,     τ   j       )            [       y        (     τ     j   +   1       )       -     y        (     τ   j     )         ]           =       ∫   0   t            Φ        (       y        (   τ   )       ,   τ     )                 y        (   τ   )                             
     The function y(τ) is a non-differentiable function, has non-bounded variation, and the transformation rules and calculation of this integral differ from the case of the differentiable function y(τ). 
     Example: calculate the integral          ∫   s   t            (       y        (   τ   )       -     y        (   s   )         )                 y        (   τ   )         .                       
     In this case          S   n     =       ∑     j   =   0     N                         [       y        (     τ     j   +   1       )       -     y        (     τ   j     )         ]          [       y        (     τ   j     )       -     y        (   s   )         ]       .                       
     Denote Δ j+1 =y(τ j+1 )−y(τ j ); s=τ 0 ; t=τ N . Then          S   n     =         ∑     j   =   1       N   -   1                         (       ∑     k   =   1     j                     Δ   k       )          Δ     j   +   1           =         1   2          [         (       ∑     k   =   1       N   -   1                       Δ   k       )     2     -       ∑     j   =   1       N   -   1                       Δ   j   2         ]       =         1   2            (       y        (   t   )       -     y        (   s   )         )     2       -       1   2            ∑     j   =   1       N   -   1                         [       y        (     τ     j   +   1       )       -     y        (     τ   j     )         ]     2                           lim          N   →   ∞              S   N       =         1   2            (       y        (   t   )       -     y        (   s   )         )     2       -       1   2            (     t   -   s     )     .                         
     For a differentiable function y(τ)            ∫   s   t            (       y        (   τ   )       -     y        (   s   )         )               y        (   τ   )             =       1   2            (       y        (   t   )       -     y        (   s   )         )     2                       
     It is possible to introduce a definition of stochastic integral that can be stable to transformation from the process with differentiable trajectories to the process with non-differentiable trajectories. 
     In the case B introduce the following definition (Stratonovich symmetrical stochastic integral):            ∫   0   t            Φ        (       y        (   τ   )       ,   τ     )                 y        (   τ   )             =         l   .   i   .   m       N   →   ∞       .       ∑     j   =   1     N                       Φ        (         y        (     τ     j   +   1       )       +     y        (     τ   j     )         2     )            [       y        (     τ     j   +   1       )       -     y        (     τ   j     )         ]                           
     or in the equivalent form:            ∫   0   t            Φ        (       y        (   τ   )       ,   τ     )                 y        (   τ   )             =           l   .   i   .   m   .       N   →   ∞              ∑     j   =   1     N                         Φ        (     y        (         τ     j   +   1       +     τ   j       2     )       )            [       y        (     τ     j   +   1       )       -     y        (     τ   j     )         ]            
            l   .   i   .   m   .       N   →   ∞            {         ∑     j   =   1     N                       Φ        (           y        (     τ     j   +   1       )       +     y        (     τ   j     )         2     ,     τ   j       )            [       y        (     τ     j   +   1       )       -     y        (     τ   j     )         ]         -       ∑     j   =   1     N                       Φ        (       y        (     τ   j     )       ,     τ   j       )            [       y        (     τ     j   +   1       )       -     y        (     τ   j     )         ]           }           =     l   .   i   .   m   .     {           ∑     j   =   1     N                         [       Φ        (         y        (     τ   j     )       +         y        (     τ     j   +   1       )       -     y        (     τ   j     )         2       ,     τ   j       )       -     Φ        (       y        (     τ   j     )       ,     τ   j       )         ]       N   →   ∞                 [       y        (     τ     j   +   1       )       -     y        (     τ   j     )         ]           }     =           l   .   i   .   m   .       N   →   ∞            1   2          {         ∑     j   =   1     N                           ∂     Φ        (       y        (     τ   j     )       ,     τ   j       )           ∂   y            [       y        (     τ     j   +   1       )       -     y        (     τ   j     )         ]       2       +       ∑     j   =   1     N                     0          (       y        (     τ     j   +   1       )       -     y        (     τ   j     )         )          [       y        (     τ     j   +   1       )       -     y        (     τ   j     )         ]             }       =     {                            1   2            ∫   0   t              ∂     Φ        (       y        (   τ   )       ,   τ     )           ∂   y                          τ           ,                                1   2            ∫   0   t              ∂     Φ        (       y        (   τ   )       ,   τ     )           ∂   y              σ   2          (       y        (   τ   )       ,   τ     )               τ                                               
     The first expression is describes the case of Brownian motion with constant diffusion coefficient, M[y(τ j+1 )−y(τ j )] 2 =τ j+1 −τ j , and the second expression describes a more general case of non homogeneous Brownian motion: 
     
       
           M{[y (τ j+1 )− y (τ j )] 2   |y (τ j )= y}=σ   2 ( y (τ j ), τ j )[τ j+1 −τ j ]+0(τ j+1−τ   j ). 
       
     
     An ordinary differential equation               y          t       =     A        (     y   ,   t     )                       
     can be considered as a limit for Δt→0 in the equation in finite differences Δy=A(y,t)Δt+o(Δt). In the case of stochastic differential equation the increment Δy include the random addend Δy=A(y,t)Δt+Φ(y,t,Δt,α t ), where α t  is independent random values; time is discrete. For limit non-degenerate stochastic disturbance 
     
       
         Δ y=A ( y,t )Δ t+f ( y,t,α   t ){square root over (Δt)}  (1) 
       
     
     The relation (1) is similar to equation described until limited model of Brownian motion (Wiener process). Process of Brownian motion can be described as limit of process with discrete set of states. Consider a stray particle on a lattice with a temporal step Δt and a spatial step δ, δ={square root over (Δt)}. During the time t=nΔt the particle displacement is            x        (   t   )       =       ∑     k   =   1     n                     Δ                   x   k           ,                   
     where Δx k =δ or −δ with the probability ½. Using the central limit theorem it is very simple to obtain that for Δt→0 the probability density of the stray process x(t) trends to Gaussian density of probability. 
     As a further example, for the sequence ξ={ξ 1 ,ξ 2 , . . . , ξ n } of mutual independent random values, similar probability partition law, mathematical expectation M[ξ i ]=a and dispersion Dξ i =b the probability density for the sum of random values          η   n     =       ∑     k   =   1     n                     ξ   k                       
     trends to Gaussian probability density function with the parameters M[η n ]=na, Dη n =nb:          P        {         η   n     -     n                 a           n                 b         }       =       1       2      π                ∫     -   ∞     z                   -     u   2       /   2                 u     .                           
     If the density function of random addends is not similar, then for application of the central probability theorem is desirable to use the Linderberg condition:          P        {       max     1   ≤   k   ≤   n            |       ξ   k     -     a   k       |     &gt;     τ          ∑     i   =   1     n                     D                   ξ   i                 }       →   0                   
     for n→∞, where τ&gt;0 is arbitrary constant number. 
     Also, the trajectories of until-limited stray convergence with the probability 1 (broken lines x Δ (t) converge in the limit to a smooth trajectory x(t)) for Δt→0). The limit random process x(t) is called a Wiener process. The trajectory of the Wiener process is piecewise:            Δ                 x     ≈       Δ                 t         ;         Δ                 x       Δ                 t       →     ±   ∞                       
     for Δt→0. With the probability 1, the trajectory x(t) is not differentiable in all points t and, at the same time, the trajectory x(t) is smoothly and satisfy of uniformly continuous condition: for small values |t 2 −t 1 |, |x(t 2 )−x(t 1 )|≦K|t 2 −t 1 | 1/2 , where K=const. Extending the axis x in {square root over (B)} times, gives the Brownian motion with the diffusion coefficient B. The Brownian motion with the drift coefficient A corresponds to the case of Brownian motion with non-equal probability of up and down transfers of the stray process on the lattice. 
     As an example, consider that the probability of up transfer is p, down is q=1−p and p≠q . Then M[Δx k ]=(p−q){square root over (BΔt)}=AΔt. In this case          p   =       1   2     +     A            Δ                 t     B             ,     q   =       1   2     -     A              Δ                 t     B       .                           
     For Δt→0 the probabilities of up and down displacements trends to ½. According to this property, (notwithstanding the infinite velocity) the mean displacement is finite during the finite time. Define all smoothly Markovian processes as the sum of large number of small increments and        {                              M        [         Δ                 x     |   x     ,   t     ]       =         A        (     x   ,   t     )          Δ                 t     +     o        (     Δ                 t     )           ,                                  M        [           (     Δ                 x     )     2     |   x     ,   t     ]       =         B        (     x   ,   t     )          Δ                 t     +     o        (     Δ                 t     )           ,                                M        [       (     Δ                 x     )     k     ]       =     o        (     Δ                 t     )                                      
     for k&gt;2. 
     For this case            lim     N   →   ∞              ∑     j   =   1     N                       [       x     j   +   1       -     x   j       ]     2         =       ∫   0   T            B        (       x        (   τ   )       ,   τ     )                 τ     .                         
     As an example of until-limited models of Brownian motion, consider the random process x Δ (t) with discrete time, t=nΔ, and with smoothly-set state:              x   Δ          (   t   )       =       ∑     j   =   1     n                       η        (     j                 Δ     )          Δ         ,                   
     where η(jΔ) are the values of a stationary Gaussian random process with the auto-correlation function R η (τ)=M[η(t)η(t+τ)]=σ 2 R(τ). The function R(τ) decreases if τ increases. Define τ cor  as the time when for the case |t 2 −t 1 |&gt;τ cor  Gaussian random values η(t 1 ) and η(t 2 ) are weakly correlated and weakly dependent, accordingly. For the sum x Δ (t) of weakly dependent Gaussian values one can use the central limit theorem. In this case it is desirable to develop the process x Δ (t) with the mathematical expectation of quadratic increment for one step Δ proportional to Δ:            M        [       {       x        (     j                 Δ     )       -     x        (       (     j   -   1     )        Δ     )         }     2     ]       =         Δ   2        D                 η     =         Δ   2          σ   2       =     Δ                 const           ;       σ   2     =       const   Δ     .                       
     In this case, the stochastic process x Δ (t) for Δ→0 turns into the process of Brownian motion. Thus for decreasing Δ=τ cor  the auto-correlation function of the stochastic process η(t) must be to change as follows: the graphic form of the function R η (τ) must simultaneously be compressed on the axis τ and stretched on the ordinate axis. The area under this curve is constant:            ∫     -   ∞       +   ∞                ℜ   η          (   τ   )               τ         =     const   =     C   .                       
     In the limit R η (τ)→Cδ(τ); δ(τ) is a Dirac delta-function. The generalized limited random process η(t) is the Gaussian δ-correlated stochastic process (white noise of level C) with constant spectral density:            S   η          (   ω   )       =         1     2      π            ∫          iωτ            ℜ   η          (   τ   )               τ           =       C     2      π       .                       
     One can define different until-limit models x Δ (t) of Brownian motion with changing of auto-correlation function types R η (τ). 
     Example 1 
     Let            S   η          (   ω   )       =     {                 C     2      π                     for                |   ω   |     &lt;     ω   0                                0   ,     |   ω   |     &gt;     ω   0                   ,                       
     where auto-correlation function is            ℜ   η          (   τ   )       =       ∫          iωτ            S   η          (   ω   )               ω         =       C   π        sin          ω   0     τ                         
     and for ω 0 →∞, R η (τ)→Cδ(τ). In this case the process          x        (   t   )       =       ∫   0   t            η        (   θ   )               θ                         
     becomes Brownian motion. 
     Example 2 
     Let            S   η          (   ω   )       =       α   2         α   2     +     ω   2                         
     and R η (τ)=αe −α|τ| →δ(τ) for α→∞. 
     The smoothly Markovian processes are connected with the process of Brownian motion and can be obtained as the solution of stochastic differential equations with the Brownian motion as external forces (diffusion processes). 
     By defining M[ƒ 2 (y,t,α t )]=B(y,t); M[ƒ(y,t,α t )]=0 in equation (1) then the density probability function p(y,t) of the stochastic solution for equation (1) is defined as the solution of Fokker-Planck-Kolmogorov equation:                  ∂     p        (     y   ,   t     )           ∂   t       =         -     ∂     ∂   y              {       A        (     y   ,   t     )            p        (     y   ,   t     )         }       +       1   2            ∂   2       ∂     y   2              {       B        (     y   ,   t     )            p        (     y   ,   t     )         }                 (   2   )                         
     In general form, stochastic differential equations can be described as:                     x   i       =       F        (       x   1     ,   …              ,     x   n     ,   t     )       +       ∑     k   =   1     n                         σ   ik          (     x   ,   t     )                   y   k          (   t   )                       (   3   )                         
     where y k (t) are independent processes of Brownian motion, or                         x   i            t       =         F   i          (     x   ,   t     )       +       ∑     k   =   1     n                         σ   ik          (     x   ,   t     )              ξ   k          (   t   )               ,           (   4   )                         
     where ξ k (t) are independent Gaussian white noises; x={x 1 ,x 2 , . . . , x n }. 
     The solutions of equations (3) and (4) can be to defined as equivalent stochastic integral equalities                x   i     =         x   i          (   0   )       +       ∫     t   0     t              F   i          (       x        (   τ   )       ,   τ     )               τ         +       ∑     k   =   1     n                       ∫     t   0     t              σ   ik          (       x        (   τ   )       ,   τ     )                   y   k          (   τ   )                         (   5   )                         
     If the stochastic integrals in equation (5) are defined as Ito stochastic integrals, then equations (3) and (4) are the stochastic Ito differential equations. If defined as the symmetrical Stratonovich integrals, then equations (3),(4) are stochastic Stratonovich differential equations. In last case it is possible to use stochastic processes ξ k (t) as wide-band Gaussian processes. 
     The Ito stochastic integral is defined as:                J   I     =         ∫   0   t            Φ        (       y        (   τ   )       ,   τ     )                   y   k          (   τ   )             =         l   .   i   .   m   .       N   →   ∞              ∑     j   =   1     N                       Φ        (       y        (     τ   j     )       ,     τ   j       )            [         y   k          (     τ     j   +   1       )       -       y   k          (     τ   j     )         ]                     (   6   )                         
     The symmetrical Stratonovich stochastic integral is defined as:                J   S     =         ∫   0   t            Φ        (       y        (   τ   )       ,   τ     )                 y        (   τ   )             =         l   .   i   .   m   .       N   →   ∞              ∑     j   =   1     N                       Φ        (           y        (     τ   j     )       +     y        (     τ     j   +   1       )         2     ;     τ   j       )            [         y   k          (     τ     j   +   1       )       -       y   k          (     τ   j     )         ]                     (   7   )                         
     The difference between these two stochastic integrals is equal to:                  J   S     -     J   I       =       1   2            ∑     l   =   1     n                         ∂   Φ       ∂     y   l                B   kl          (       y        (   τ   )       ,   τ     )               τ                   (   8   )                         
     If the functions Φ(y,t) independent from y then both definitions of stochastic integral are equivalent:            ∂   Φ       ∂   y       ≡   0                   
     and J S ≡J 1 . 
     Equations (3) and (4) define Markovian process. From definition (5), it is clear that the probability distribution for x(t), t&gt;t 0  and defined initial states x(t 0 )∈X 0  are dependent only from the states x(t 0 ) and are independent from past before the moment t 0 , while          x   i     =         x   i          (   0   )       +       ∫     t   0     t              F   i          (       x        (   τ   )       ,   τ     )               τ         +       ∑     k   =   1     n                       ∫     t   0     t              σ   ik          (       x        (   τ   )       ,   τ     )                   y   k          (   τ   )                                 
     and y k (τ) have independent from past the values before the moment t 0 . 
     Markovian process can be fully characterized by local characteristics: 
     
       
           M[x   i ( t+Δt )− x   i ( t )| x,t]=A   i ( x,t )Δ t+o (Δ t ), 
       
     
     
       
           M [( x   i ( t+Δt )− x   i ( t ))( x   j ( t+Δt )− x   j ( t ))| x,t]=B   ij ( x,t )Δ t+o (Δ t ). 
       
     
     For Ito stochastic differential equations              A   i          (     x   ,   t     )       =       F   i          (     x   ,   t     )         ;         B   ij          (     x   ,   t     )       =       ∑     k   =   1     n                         σ   ik          (     x   ,   t     )              σ   jk          (     x   ,   t     )                             
     Using the relation between Ito and Stratonovich integrals from equation (8) it is possible to obtain for symmetrical stochastic differential equations:              A   i          (     x   ,   t     )       =         F   i          (     x   ,   t     )       +       1   2            ∑     k   =   1     n                         ∂       σ   ik          (     x   ,   t     )           ∂     x   j              σ   jk          (     x   ,   t     )               ;               B   ik          (     x   ,   t     )       =       ∑     k   =   1     n                         σ   ik          (     x   ,   t     )                σ   jk          (     x   ,   t     )       .                         
     The density probability function can be defined as the solution of equation (2).