# Modeling, Simulation, and Cruise Characteristics of Wingtip-Jointed Composite Aircraft
## 3 Multibody Dynamic Equation of the Composite Aircraft System  
According to the established dynamic model of the wingtip-jointed composite aircraft system, the simulation platform was built based on MATLAB/Simulink with a multibody system state module, a multibody dynamics solver module, a force model calculation module, an automatic control module, and a record and report module, as shown in Figure 8.  
The multibody system state module mainly takes charge of the corresponding parameters including mass, static moment, and rotation tensor of the augmented body under different real-time relative roll angles (\(\varphi_{12}\)). In the force model calculation module, the aerodynamic force and moment are calculated based on the multibody system state and the real-time motion parameters. The multibody dynamics solver module mainly takes charge of accepting the input parameters from the multibody system state module and force model calculation module. The automatic control module mainly conducts the design work of control strategy based on the real-time errors of the aircraft system's position, posture, and velocity. The record and report module mainly saves the data and display in the scope at every iteration. The iterative format was selected as ode45 and the step size was 0.01 s.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Aerodynamic Parameters** & **Symbol** & **Data Acquisition Method** \\ \hline Aerodynamic derivatives of & & \\ relative roll motion & & \\ \cline{1-2} Aerodynamic derivatives of & & \\ \cline{1-2} Aerodynamic derivatives of & & \\ composite control surface & & \\ deflection & & \\ \cline{1-2}  &  
The dynamic simulation platform of the composite aircraft system was built based on the equations with total parameter use, such that the dynamic response of the single- and composite-trimming strategies could be carried out. The single-trimming strategy refers to each control surface deflection of the composite aircraft needing to meet the composite requirements. The overall motion dynamic equation of the aircraft system is balanced, and there is no need to satisfy the control input scheme of the internal relative motion dynamic equation. The composite-trimming strategy means that the control input of each control surface deflection of the composite aircraft system needs to meet the balance of the overall motion and internal relative motion dynamic equations of the composite aircraft system. Detailed parameters and corresponding numbers are listed in Table 3.  
According to the simulation results of the compound flight dynamics response with the single-trimming strategy, the system dynamics simulation of the composite aircraft is terminated at 4.59 s when the relative roll angle reaches 180 degrees; that is, the two composite aircraft finally collide in the form of relative roll motion at 4.59 s, through the wing tip hinge mechanism. In contrast to the single aircraft flight dynamics response, the relative roll moment exists in composite flight, which results in an internal relative roll motion. It is necessary to deflect the aileron, elevator, or rudder, in order to balance the relative roll moment in the system internal dynamic equation. Differential dual elevators cause redundant pitching torque, which makes the balancing problem of the composite aircraft more complex. The angle of differential rudder causes an internal relative