take off analysis of the olympic ski jumping competition hs 106m abstract the take off phase approximately 6 m of the jumps of all athletes participating in the individual hs 106 m hill ski jumping competition at the torino olympics was filmed with two high speed cameras the high altitude of the pragelato ski jumping venue 1600 m and slight tail wind in the final jumping round were expected to affect the results of this competition the most significant correlation with the length of the jump was found in the in run velocity r 0 628 p n 50 this was a surprise in olympic level ski jumping and suggests that good jumpers simply had smaller friction between their skis and the in run tracks and or the aerodynamic quality of their in run position was better angular velocity of the hip joint of the best jumpers was also correlated with jumping distance r 0 651 p n 10 the best jumpers in this competition exhibited very different take off techniques but still they jumped approximately the same distance this certainly improves the interests in ski jumping among athletes and spectators the comparison between the take off techniques of the best jumpers showed that even though the more marked upper body movement creates higher air resistance it does not necessarily result in shorter jumping distance if the exposure time to high air resistance is not too long a comparison between the first and second round jumps of the same jumpers showed that the final results in this competition were at least partly affected by the wind conditions

adjustments to zatsiorsky seluyanov s segment inertia parameters zatsiorsky et al in contemporary problems in biomechanics pp 272 291 crc press massachusetts 1990a obtained by means of a gamma ray scanning technique the relative body segment masses center of mass cm positions and radii of gyration for samples of college aged caucasian males and females although these data are the only available and comprehensive set of inertial parameters regarding young adult caucasians they have been rarely utilized for biomechanical analyses of subjects belonging to the same or a similar population the main reason is probably that zatsiorsky et al used bony landmarks as reference points for locating segment cms and defining segment lengths some of these landmarks were markedly distant from the joint centers currently used by most researchers as reference points the purpose of this study was to adjust the mean relative cm positions and radii of gyration reported by zatsiorsky et al in order to reference them to the joint centers or other commonly used landmarks rather than the original landmarks the adjustments were based on a number of carefully selected sources of anthropometric data

some applications of miller mocanu lemma on certain classes of meromorphic functions in this paper making use of a linear operator we introduce and study certain new classes of meromorphic functions we derive some inclusion results these classes contain many known classes as a special case

lagrangian coherent structures and mixing in two dimensional turbulence abstract we introduce a lagrangian definition for the boundaries of coherent structures in two dimensional turbulence the boundaries are defined as material lines that are linearly stable or unstable for longer times than any of their neighbors such material lines are responsible for stretching and folding in the mixing of passive tracers we derive an analytic criterion that can be used to extract coherent structures with high precision from numerical or experimental data sets the criterion provides a rigorous link between the lagrangian concept of hyperbolicity the okubo weiss criterion and vortex boundaries we apply the results to simulations of two dimensional barotropic turbulence

a sharper bonferroni procedure for multiple tests of significance summary a simple procedure for multiple tests of significance based on individual p values is derived this simple procedure is sharper than holm s 1979 sequentially rejective procedure both procedures contrast the ordered p values with the same set of critical values holm s procedure rejects an hypothesis only if its p value and each of the smaller p values are less than their corresponding critical values the new procedure rejects all hypotheses with smaller or equal p values to that of any one found less than its critical value

an efficient exponential time integration method for the numerical solution of the shallow water equations on the sphere the exponential propagation methods were applied in the past for accurate integration of the shallow water equations on the sphere despite obvious advantages related to the exact solution of the linear part of the system their use for the solution of practical problems in geophysics has been limited because efficiency of the traditional algorithm for evaluating the exponential of jacobian matrix is inadequate in order to circumvent this limitation we modify the existing scheme by using the incomplete orthogonalization method instead of the arnoldi iteration we also propose a simple strategy to determine the initial size of the krylov space using information from previous time instants this strategy is ideally suited for the integration of fluid equations where the structure of the system jacobian does not change rapidly between the subsequent time steps a series of standard numerical tests performed with the shallow water model on a geodesic icosahedral grid shows that the new scheme achieves efficiency comparable to the semi implicit methods this fact combined with the accuracy and the mass conservation of the exponential propagation scheme makes the presented method a good candidate for solving many practical problems including numerical weather prediction

dynamic stability and compensatory stepping responses during anterior gait slip perturbations in people with chronic hemiparetic stroke abstract to examine the control of dynamic stability and characteristics of the compensatory stepping responses to an unexpected anterior gait slip induced under the non involved limb in people with hemi paretic stroke pwhs and to examine any resulting adaptive changes in these on the second slip due to experience from prior slip exposure ten pwhs experienced overground slip s1 during walking on the laboratory walkway after 5 8 regular walking rw trials followed by a second consecutive slip trial s2 the slip outcome backward loss of balance blob and no loss of balance nlob and com state i e its com position and velocity stability were examined between the rw and s1 and s1 and s2 at touchdown td of non involved limb and at liftoff lo of the contralateral limb at td there was no difference in stability between rw and s1 however at lo subjects demonstrated a lower stability on s1 than rw resulting in a 100 backward loss of balance blob with compensatory stepping response recovery step rs 4 10 or aborted step as 6 10 on s2 although there was no change in stability at td there was a significant improvement in stability at lo with a 40 decrease in blob there was also a change in step strategy with a decrease in as response 60 to 35 p

validation of net joint loads calculated by inverse dynamics in case of complex movements application to balance recovery movements the joint forces and moments driving the motion of a human subject are classically computed by an inverse dynamic calculation however even if this process is theoretically simple many sources of errors may lead to huge inaccuracies in the results moreover a direct comparison with in vivo measured loads or with gold standard values from literature is only possible for very specific studies therefore assessing the inaccuracy of inverse dynamic results is not a trivial problem and a simple method is still required this paper presents a simple method to evaluate both 1 the consistency of the results obtained by inverse dynamics 2 the influence of possible modifications in the inverse dynamic hypotheses this technique concerns recursive calculation performed on full kinematic chains and consists in evaluating the loads obtained by two different recursive strategies it has been applied to complex 3d whole body movements of balance recovery a recursive newton euler procedure was used to compute the net joint loads two models were used to represent the subject bodies considering or not the upper body as a unique rigid segment the inertial parameters of the body segments were estimated from two different sets of scaling equations de leva p 1996 adjustments to zatsiorsky suleyanov s segment inertia parameters journal of biomechanics 29 1223 1230 dumas r cheze l verriest j p 2006b adjustments to mcconville et al and young et al body segment inertial parameters journal of biomechanics in press using this comparison technique it has been shown that for the balance recovery motions investigated 1 the use of the scaling equations proposed by dumas et al instead of those proposed by de leva improves the consistency of the results average relative influence up to 30 for the transversal moment 2 the arm motions dynamically influence the recovery motion in a non negligible way average relative influence up to 15 and 30 for the longitudinal force and the transversal moment respectively

a new geometric based model to accurately estimate arm and leg inertial estimates segment estimates of mass center of mass and moment of inertia are required input parameters to analyze the forces and moments acting across the joints the objectives of this study were to propose a new geometric model for limb segments to evaluate it against criterion values obtained from dxa and to compare its performance to five other popular models twenty five female and 24 male college students participated in the study for the criterion measures the participants underwent a whole body dxa scan and estimates for segment mass center of mass location and moment of inertia frontal plane were directly computed from the dxa mass units for the new model the volume was determined from two standing frontal and sagittal photographs each segment was modeled as a stack of slices the sections of which were ellipses if they are not adjoining another segment and sectioned ellipses if they were adjoining another segment e g upper arm and trunk length of axes of the ellipses was obtained from the photographs in addition a sex specific non uniform density function was developed for each segment a series of anthropometric measurements were also taken by directly following the definitions provided of the different body segment models tested and the same parameters determined for each model comparison of models showed that estimates from the new model were consistently closer to the dxa criterion than those from the other models with an error of less than 5 for mass and moment of inertia and less than about 6 for center of mass location

whole body inverse dynamics over a complete gait cycle based only on measured kinematics this paper presents a three dimensional 3d whole body multi segment model for inverse dynamics analysis over a complete gait cycle based only on measured kinematic data the sequence of inverse dynamics calculations differs significantly from the conventional application of inverse dynamics using force plate data a new validated smooth transition assumption was used to solve the indeterminacy problem in the double support phase kinematic data is required for all major body segments and hence a whole body gait measurement protocol is presented finally sensitivity analyses were conducted to evaluate the effects of digital filtering and body segment parameters on the accuracy of the prediction results the model gave reasonably good estimates of sagittal plane ground forces and moment however the estimates in the other planes were less good which we believe is largely due to their small magnitudes in comparison to the sagittal forces and moment the errors observed are most likely caused by errors in the kinematic data resulting from skin movement artefact and by errors in the estimated body segment parameters a digital filtering cut off frequency of 4 5 hz was found to produce the best results it was also shown that errors in the mass properties of body segments can play a crucial role with changes in properties sometimes having a disproportionate effect on the calculated ground reactions the implication of these results is that even when force plate data is available the estimated joint forces are likely to suffer from similar errors

lower extremity control during turns initiated with and without hip external rotation the pirouette turn is often initiated in neutral and externally rotated hip positions by dancers this provides an opportunity to investigate how dancers satisfy the same mechanical objectives at the whole body level when using different leg kinematics the purpose of this study was to compare lower extremity control strategies during the turn initiation phase of pirouettes performed with and without hip external rotation skilled dancers n 5 performed pirouette turns with and without hip external rotation joint kinetics during turn initiation were determined for both legs using ground reaction forces grfs and segment kinematics hip muscle activations were monitored using electromyography using probability based statistical methods variables were compared across turn conditions as a group and within dancer despite differences in grfs and impulse generation between turn conditions at least 90 of each grf was aligned with the respective leg plane a majority of the net joint moments at the ankle knee and hip acted about an axis perpendicular to the leg plane however differences in shank alignment relative to the leg plane affected the distribution of the knee net joint moment when represented with respect to the shank versus the thigh during the initiation of both turns most participants used ankle plantar flexor moments knee extensor moments flexor and abductor moments at the push leg s hip and extensor and abductor moments at the turn leg s hip representation of joint kinetics using multiple reference systems assisted in understanding control priorities

inclusion properties for certain classes of meromorphic functions associated with the choi saigo srivastava operator abstract the purpose of the present paper is to introduce several new classes of meromorphic functions defined by using a meromorphic analogue of the choi saigo srivastava operator for analytic functions and investigate various inclusion properties of these classes some interesting applications involving these and other classes of integral operators are also considered

the boundary constraint method for constructing vortex surface fields we develop a boundary constraint method for constructing the vortex surface field vsf in a three dimensional fluid velocityvorticity field the isosurface of the vsf is a vortex surface consisting of vortex lines which can be used to characterize the evolution of vortical structures in a lagrangian sense the evolution equation with pseudo time is solved under the vsf boundary constraint to obtain a numerical solution of the vsf compared with the existing two time method the boundary constraint method constructs the vsf from a single velocity dataset at a given time instead of a time series of velocity fields starting from a simple condition this improvement significantly increases the applicability of the vsf method and reduces the demanding computational cost and required velocity data size using the boundary constraint method we construct the vsfs in taylorgreen flow and transitional channel flow in addition the uniqueness of the vsf solution is discussed and the convergence of the error in the calculation of vsfs is analyzed

knee and ankle joint torque angle relationships of multi joint leg extension abstract the force length relation f l r is an important property of skeletal muscle to characterise its function whereas for in vivo human muscles torque angle relationships t a r represent the maximum muscular capacity as a function of joint angle however since in vivo force torque length data is only available for rotational single joint movements the purpose of the present study was to identify torque angle relationships for multi joint leg extension therefore inverse dynamics served for calculation of ankle and knee joint torques of 18 male subjects when performing maximum voluntary isometric contractions in a seated leg press measurements in increments of 10 knee angle from 30 to 100 knee flexion resulted in eight discrete angle configurations of hip knee and ankle joints for the knee joint we found an ascending descending t a r with a maximum torque of 289 5 43 3 n m which closely matches literature data from rotational knee extension in comparison to literature we observed a shift of optimum knee angle towards knee extension in contrast the t a r of the ankle joint vastly differed from relationships obtained for isolated plantar flexion for the ankle t a r derived from multi joint leg extension subjects operated over different sections of the force length curve but the ankle t a r derived from isolated joint efforts was over the ascending limb for all subjects moreover mean maximum torque of 234 7 56 6 n m exceeded maximal strength of isolated plantar flexion 185 7 27 8 n m from these findings we conclude that muscle function between isolated and more physiological multi joint tasks differs this should be considered for ergonomic and sports optimisation as well as for modelling and simulation of human movement

some inclusion properties of a certain family of integral operators abstract the authors introduce several new subclasses of analytic functions which are defined by means of a general integral operator i and investigate various inclusion properties of these subclasses many interesting applications involving these and other families of integral operators are also considered

estimation of centre of gravity movements in sitting posture application to trunk backward tilt abstract the aim of this study was to highlight in sitting posture the value of distinguishing between the movements of the vertical projection of the centre of gravity cgv and its difference from the centre of pressure cp cgv a protocol for healthy young trained adults consisting in tilting their trunk backward or keeping it vertical was used a frequency analysis shows that statistically significant effects were only seen on cp cgv movements the rms increased by 37 p 0 004 while the mpf decreased by 5 p 0 016 suggesting an increased muscular activity in these tilting postures in contrast no statistically significant effects on cp and cgv were reported these data highlight the advantage in sitting posture of splitting overall cp displacements into basic components i e cgv and cp cgv each of them having a biomechanical significance

moving beyond quiet stance applicability of the inverted pendulum model to stooping and crouching postures background currently it is unknown whether the inverted pendulum model is applicable to stooping or crouching postures therefore the aim of this study was to determine the degree of applicability of the inverted pendulum model to these postures via examination of the relationship between the centre of mass com acceleration and centre of pressure cop com difference methods ten young adults held static standing stooping and crouching postures each for 20 s for both the anterior posterior ap and medio lateral ml directions the time varying com acceleration and the cop com were computed and the relationship between these two variables was determined using pearson s correlation coefficients additionally in both directions the average absolute com acceleration average absolute cop com signal and the inertial component i e i wh were compared across postures results pearson correlation coefficients revealed a significant negative relationship between the com acceleration and cop com signal for all comparisons regardless of the direction p 0 001 while no effect of posture was observed in the ap direction p 0 463 in the ml direction the correlation coefficients for stooping were different i e stronger than standing p 0 008 regardless of direction the average absolute com acceleration for both the stooping and crouching postures was greater than standing p 0 002 conclusion the high correlations indicate that the inverted pendulum model is applicable to stooping and crouching postures due to their importance in completing activities of daily living there is merit in determining what type of motor strategies are used to control such postures and whether these strategies change with age

an algorithm for determining gravity line location from posturographic recordings abstract in posturographic recordings the center of pressure cop displacement does not accurately reflect migration of the gravity line gl the vertical line passing through the body s center of gravity cog since the horizontal ground reaction force f x is proportional to the horizontal acceleration of the cog its second integral does represent the horizontal position of the gravity line glp however the initial constants of integration initial velocity and position are not known in this note a technique for estimating these integration constants is suggested zero point to zero point integration this method is based on a postulation that when f x 0 the glp and cop coincide by integrating f x from one zero point to another zero point both the instantaneous glp and its velocity are determined a validation of the suggested algorithm was performed using optical methods to determine the glp during a one legged standing tasks cross correlation values of glp determined via videography and the suggested algorithm ranged from 0 79 to 0 96 these results suggest that the zero point to zero point integration is an acceptable technique for determining glp from posturographic recordings

lower extremity control and dynamics during backward angular impulse generation in forward translating tasks observation of complex whole body movements suggests that the nervous system coordinates multiple operational subsystems using some type of hierarchical control when comparing two forward translating tasks performed with and without backward angular impulse we have learned that both trunk leg coordination and reaction force time characteristics are significantly different between tasks this led us to hypothesize that differences in trunk leg coordination and reaction force generation would induce between task differences in the control of the lower extremity joints during impulse generation phase of the tasks eight highly skilled performers executed a series of forward jumps with and without backward rotation reverse somersault and reverse timer respectively sagittal plane kinematics reaction forces and electromyograms of lower extremity muscles were acquired during the take off phase of both tasks lower extremity joint kinetics were calculated using inverse dynamics the results demonstrated between task differences in the relative angles between the lower extremity segments and the net joint forces reaction force and the joint angular velocity profiles significantly less knee extensor net joint moments and net joint moment work and greater hip extensor net joint moments and net joint moment work were observed during the push interval of the reverse somersault as compared to the reverse timer between task differences in lower extremity joint kinetics were regulated by selectively activating the bi articular muscles crossing the knee and hip these results indicate that between task differences in the control of the center of mass relative to the reaction force alters control and dynamics of the multijoint lower extremity subsystem

a linear operator and associated families of meromorphically multivalent functions making use of a linear operator which is defined here by means of the hadamard product or convolution the authors introduce and investigate the various properties and characteristics of two novel families of meromorphically multivalent functions they also extend the familiar concept of neighborhoods of analytic functions to these subclasses of meromorphically multivalent functions

effects of age and step length on joint kinetics during stepping task following a balance perturbation a stepping response is commonly used to regain support and the distance of the recovery step can vary to date no other studies have examined joint kinetics in young and old adults during increasing step distances when participants are required to bring their rear foot forward therefore the purpose of this study was to examine age related differences in joint kinetics with increasing step distance twenty young and 20 old adults completed the study participants completed a step starting from double support at an initial distance equal to the individual s average step length the distance was increased by 10 body height until an unsuccessful attempt a one way repeated measures anova was used to determine the effects of age on joint kinetics during the maximum step distance a two way repeated measures mixed model anova was used to determine the effects of age step distance and their interaction on joint kinetics during the first three step distances for all participants young adults completed a significantly longer step than old adults during the maximum step in general kinetic measures were greater in the young than in the old as step distance increased all but one kinetic measure increased for both young and old adults this study has shown the ability to discriminate between young and old adults and could potentially be used in the future to distinguish between fallers and non fallers

are the maximum shortening velocity and the shape parameter in a hill type model of whole muscle related to activation abstract mathematical models of the inter relationship of muscle force velocity and activation are useful in forward dynamic simulations of human movement tasks the objective of this work was to determine whether the parameters maximum shortening velocity v max and shape parameter k of a hill type muscle model interrelating muscle force velocity and activation are themselves dependent on the activation to fulfill this objective surface emg signals from four muscles as well as the kinematics and kinetics of the arm were recorded from 14 subjects who performed rapid release elbow extension tasks at 25 50 75 and 100 activation mvc the experimental elbow flexion angle was tracked by a forward dynamic simulation of the task in which v max and k of the triceps brachii were varied at each activation level to minimize the difference between the simulated and experimental elbow flexion angle because a preliminary analysis demonstrated no dependency of k on activation additional simulations were performed with constant k values of 0 15 0 20 and 0 25 the optimized values of v max normalized to the average value within a subject were then regressed onto the activation normalized v max depended significantly on the activation p k furthermore the estimated v max values were not sensitive to the selected k value the results support the use of hill type models in which v max depends on activation in forward dynamic simulations modeling muscles with mixed fiber type composition recruited in the range of 25 100 activation the use of more accurate models will lend greater confidence to the results of forward dynamic simulations

corner height influences center of mass kinematics and path trajectory during turning despite the prevalence of directional changes during every day gait relatively little is known about turning compared to straight gait while the center of mass com movement during straight gait is well characterized the com trajectory and the factors that influence it are less established for turning this study investigated the influence of a corner s height on the com trajectory as participants walked around the corner ten participants 25 3 3 74 years performed both 90 step and spin turns to the left at self selected slow normal and fast speeds while walking inside a marked path a pylon was placed on the inside corner of the path four different pylon heights were used to correspond to heights of everyday objects 0 cm no object 63 cm box crate 104 cm desk table counter 167 cm shelf cabinet obstacle height was found to significantly affect the com trajectory taller obstacles resulted in more distance between the corner and the com and between the corner and the cop taller obstacles also were associated with greater curvature in the com trajectory indicating a smaller turning radius despite the constant 90 corner taller obstacles correlated to an increased required coefficient of friction rcof due to the smaller turning radii taller obstacles also tended towards greater mediolateral ml com cop angles contrary to the initial hypothesis additionally the com was found to remain outside the base of support bos for the entire first half of stance phase for all conditions indicating a high risk of falls resulting from slips

on the relevance of residual force enhancement for everyday human movement abstract although residual force enhancement rfe i e enhanced force after active muscle stretch is shown to be present in voluntarily activated human muscles its relevance for everyday human movement is still elusive natural human motion is mainly composed of voluntarily submaximally activated muscle contractions driving coordinated multi joint movements up to now there has been no study that directly investigated the presence of rfe following stretch when performing a submaximal multi joint movement for this purpose n 13 subjects performed feedback controlled bilateral leg extensions at the level of 30 maximum voluntary activation in a motor driven leg press dynamometer isometric eccentric isometric and purely isometric contractions were arranged in a randomized experimental protocol kinematics forces and muscular activity were measured using optical motion tracking 3d force plates and emg of 9 lower extremity muscles anova identified significant rfe of external reaction force and knee extension and plantar flexion torque calculated by inverse dynamics enhanced force and torque ranged between 3 and 22 and was present for up to 22 s post stretch in spite of motor redundancy for solving a given task no differences between contraction conditions were observed for any of the analyzed muscles except for tibialis anterior on the basis of our results rfe is present in everyday alike human movement and might be an evolutionary optimization mechanism to enhance muscular performance at a given amount of energetic effort

predictive regression modeling of body segment parameters using individual based anthropometric measurements abstract body segment parameters such as segment mass center of mass and radius of gyration are used as inputs in static and dynamic ergonomic and biomechanical models used to predict joint and muscle forces and to assess risks of musculoskeletal injury previous work has predicted body segment parameters bsps in the general population using age and obesity levels as statistical predictors merrill et al 2017 estimated errors in the prediction of bsps can be as large as 40 depending on age and the prediction method employed durkin and dowling 2003 thus more accurate and representative segment parameter inputs are required for attempting to predict modeling outputs such as joint contact forces muscle forces and injury risk in individuals this study aims to provide statistical models for predicting torso thigh shank upper arm and forearm segment parameters in working adults using whole body dual energy x ray absorptiometry dxa scan data along with a set of anthropometric measurements the statistical models were developed on a training data set and independently validated on a separate test data set the predicted bsps in validation data were on average within 5 of the actual in vivo dxa based bsps while previously developed predictions de leva 1996 had average errors of up to 60 indicating that the new models greatly increase the accuracy in predicting segment parameters these final developed models can be used for calculating representative bsps in individuals for use in modeling applications dependent on these parameters

implementation of high order spline interpolations for tracking test particles in discretized fields a systematic approach for constructing high order spline interpolation methods is proposed for fields known on regular rectangular grids these interpolation methods are tested in tracking trajectories of particles submitted to a force that derives from a potential known on a grid the interplay between the time advancement scheme and the spatial interpolation is studied in detail and it is shown how the order of the trajectory solver is directly affected by the order of the spline interpolation it is also shown how an interpolation method that preserves topological properties of physical fields can be better exploited with these higher order spline approximations

does the anthropometric model influence whole body center of mass calculations in gait examining whole body center of mass com motion is one of method being used to quantify dynamic balance and energy during gait one common method for estimating the com position is to apply an anthropometric model to a marker set and calculate the weighted sum from known segmental com positions several anthropometric models are available to perform such a calculation however to date there has been no study of how the anthropometric model affects whole body com calculations during gait this information is pertinent to researchers because the choice of anthropometric model may influence gait research findings and currently the trend is to consistently use a single model in this study we analyzed a single stride of gait data from 103 young adult participants we compared the whole body com motion calculated from 4 different anthropometric models plagenhoef et al 1983 winter 1990 de leva 1996 pavol et al 2002 we found that anterior posterior motion calculations are relatively unaffected by the anthropometric model however medial lateral and vertical motions are significantly affected by the use of different anthropometric models our findings suggest that the researcher carefully choose an anthropometric model to fit their study populations when interested in medial lateral or vertical motions of the com our data can provide researchers a priori information on the model determination depending on the particular variable and how conservative they may want to be with com comparisons between groups

exploration of the validity of the two dimensional sagittal plane assumption in modeling the standing long jump most previous standing long jump studies have been based on the assumption of two dimensional sagittal plane motion with bilateral symmetry the purpose of this study was to investigate the validity of this assumption standing long jump trials were collected using six adult male participants each participant stood with a foot on each of two force plates and performed eight standing long jumps for maximal distance inverse dynamics analyses were performed for two dimensional 2d and three dimensional 3d models and joint moments powers and work values were compared the differences between these models with respect to the validity of the common planar jumping assumption were analyzed good agreement was observed between 2d and 3d methods for the lower body with minimal differences in sagittal plane moments power and work for the ankle knee and lower back there were significant but relatively small differences in the sagittal plane kinematics and kinetics at the hip for the upper body the results contradicted the sagittal plane assumption in that significant moments and power were generated about the abduction adduction axis of the shoulder and a similar amount of work was performed about both abduction adduction and flexion extension axes of the shoulder the elbow also showed significant differences in power and work these results indicate that an assumption of planar motion should be sufficient for many studies of the standing long jump that only examine lower body movement however for studies that include upper body motion diagnosing injury risk or investigating gender differences a 3d model may be more appropriate

a comparison of muscle energy models for simulating human walking in three dimensions the popular hill model for muscle activation and contractile dynamics has been extended with several different formulations for predicting the metabolic energy expenditure of human muscle actions these extended models differ considerably in their approach to computing energy expenditure particularly in their treatment of active lengthening and eccentric work but their predictive abilities have never been compared in this study we compared the predictions of five different hill based muscle energy models in 3d forward dynamics simulations of normal human walking in a data tracking simulation that minimized muscle fatigue the energy models predicted metabolic costs that varied over a three fold range 2 45 7 15 j m kg with the distinction arising from whether or not eccentric work was subtracted from the net heat rate in the calculation of the muscle metabolic rate in predictive simulations that optimized neuromuscular control to minimize the metabolic cost all five models predicted similar speeds step lengths and stance phase durations however some of the models predicted a hip circumduction strategy to minimize metabolic cost while others did not and the accuracy of the predicted knee and ankle angles and ground reaction forces also depended on the energy model used the results highlights the need to clarify how eccentric work should be treated when calculating muscle energy expenditure the difficulty in predicting realistic metabolic costs in simulated walking even with a detailed 3d musculoskeletal model the potential for using such models to predict energetically optimal gait modifications and the room for improvement in existing muscle energy models and locomotion simulation frameworks

influence of body segments parameters estimation models on inverse dynamics solutions during gait the purpose of the present study was to examine the in uence of anthropometric data on joint kinetics during gait we particularly focused on the sensitivity of inverse dynamics solutions to the use of models for body segment parameters bsp estimation six often used estimation models were selected to provide bsp values for the three segments of the lower limb kinematics and dynamics were sampled from seven subjects performing barefoot gait at three different speeds joint kinetics were estimated with the bottom up method using bsp values derived from each estimation model as anthropometric inputs the bsp estimates were highly sensitive to the model used with deviations ranging from at least 9 73 up to 60 maximal variations of peak values for the hip joint exion extension moment during the swing phase were 20 11 hence our ndings suggest that the in uence of bsp cannot be neglected observed deviations are especially due to the effect of varying simultaneously the mass moments of inertia and the center of mass location values according to the underlying relationship of interdependency linking each component considering both the differences found in joint kinetics and the level of accuracy of bsp models evidence is provided that using multiple regression bsp estimation functions derived from zatsiorsky and seluyanov biomechanics viii b 1983 pp 1152 1159 should be recommended to assess joint kinetics

a new method for estimating joint parameters from motion data joint centers and axes of rotation joint parameters are central to all branches of movement analysis in gait analysis the standard protocol used to determine hip and knee joint parameters is prone to errors arising from palpation anthropometric regression equations and misplaced alignment devices several alternative methods have been proposed but to date none have been shown to be accurate and reliable enough for use in the clinical setting this article describes a new method for joint parameter estimation the new method can be summarized as follows i the motions of two adjacent segments spanning a single joint are tracked ii the axis of rotation between every pair of observed segment configurations is computed iii the most likely intersection of all axes effective joint center and most likely orientation of the axes effective joint axis is found initial validation of the method was conducted on a hinged mechanical analog and a single healthy adult subject for the analog the center was found to be within 3 8 mm of the geometric center and 2 0 degrees of the geometric axis standard deviation for the adult subject hip centers varied on the order of 1 3 mm knee centers by 3 9 mm and knee axes by 2 0 degrees the results suggest that the new method is an objective precise and practical alternative to the standard clinical approach

predicting dynamic postural instability using center of mass time to contact information our purpose was to determine whether spatiotemporal measures of center of mass motion relative to the base of support boundary could predict stepping strategies after upper body postural perturbations in humans we expected that inclusion of center of mass acceleration in such time to contact ttc calculations would give better predictions and more advanced warning of perturbation severity ttc measures were compared with traditional postural variables which do not consider support boundaries and with an inverted pendulum model of dynamic stability developed by hof et al 2005 the condition for dynamic stability journal of biomechanics 38 1 8 a pendulum was used to deliver sequentially increasing perturbations to 10 young adults who were strapped to a wooden backboard that constrained motion to sagittal plane rotation about the ankle joint subjects were instructed to resist the perturbations stepping only if necessary to prevent a fall peak center of mass and center of pressure velocity and acceleration demonstrated linear increases with postural challenge in contrast boundary relevant minimum ttc values decreased nonlinearly with postural challenge enabling prediction of stepping responses using quadratic equations when ttc calculations incorporated center of mass acceleration the quadratic fits were better and gave more accurate predictions of the ttc values that would trigger stepping responses in addition ttc minima occurred earlier with acceleration inclusion giving more advanced warning of perturbation severity our results were in agreement with ttc predictions based on hof s model and suggest that ttc may function as a control parameter influencing the postural control system s decision to transition from a stationary base of support to a stepping strategy

effects of low pass filter combinations on lower extremity joint moments in distance running abstract inverse dynamics is a standard tool in biomechanics which requires low pass filtering of external force and kinematic signals unmatched filtering procedures are reported to affect joint moment amplitudes in high impact movements like landing or cutting but are also common in the analysis of distance running we analyzed the effects of cut off frequencies in 94 rearfoot runners at a speed of 3 5 m s additionally we investigated whether the evaluation of footwear interventions is affected by the choice of cut off frequencies we performed 3d inverse dynamics for the hip knee and ankle joints using different low pass filter cut off frequency combinations for a recursive fourth order butterworth filter we observed fluctuations of joint moment curves in the first half of stance which were most pronounced for the most unmatched cut off frequency combination kinematics 10 hz ground reaction forces grfs 100 hz and for more proximal joints peak sagittal plane hip joint moments were altered by 94 on average we observed a change in the ranking of subjects based on joint moment amplitude we found significant p

limits of recovery against slip induced falls while walking abstract slip induced falls in gait often have devastating consequences the purposes of this study were 1 to select the determinants that can best discriminate the outcomes recoveries or falls of an unannounced slip induced in gait and to find their corresponding threshold i e the limits of recovery which can clearly separate these two outcomes and 2 to verify these results in a subset of repeated slip trials based on the data collected from 69 young subjects during a slip induced in gait nine different ways of combining the center of mass com stability the hip height and its vertical velocity were investigated with the aid of logistic regression the results revealed that the com stability s and limb support represented by the quotient of hip vertical velocity to hip height s hip recorded at the instant immediately prior to the recovery step touchdown were sufficiently sensitive to account for all 100 variance in falls and specific enough to account for nearly all 98 3 variability in recoveries this boundary s hip 0 22 s 0 25 which quantifies the risk of falls in the stability limb support quotient s s hip domain was fully verified using second slip and third slip trials n 76 with classification of falls at 100 and recoveries at 98 6 the severity of an actual fall is likely to be greater further below the boundary while the likelihood of a fall diminishes above it finally the slope of the boundary also indicates the tradeoff between the stability and limb support whereby high stability can compensate for the insufficiency in limb support or vice versa

influence of body segment parameter estimation on calculated ground reaction forces in highly dynamic movements the effect of body segment parameter estimation bsp on the inverse dynamics modelling results has not yet been demonstrated in specific groups during athletic movements with high segment accelerations therefore the purpose of this study was to analyse this effect in ski jumpers as representatives of a specific group i e low body mass index by comparing calculated and measured ground reaction forces during ski jumping imitation jumps full body kinematics and vertical ground reaction forces were recorded of 9 ski jumpers performing three imitation jumps each bsp were estimated using three previously published one individually optimized and one ski jumper group specific model vertical ground reaction forces were calculated using the vertical acceleration of the segments as well as the bsp of the single models in a top down approach statistical analysis revealed a main model effect concerning the root mean square error between the calculated and the measured ground reaction force with deviations between the models of 53 individual optimization and the application of the ski jumper group specific model increased the accuracy of the calculated ground reaction forces by 11 and 7 respectively compared to the best performing published model the results of inverse dynamics modelling are very sensitive to the bsp estimation for specific groups like ski jumpers during movements incorporating high segment accelerations this emphasizes the importance of selecting adequate bsp estimation models or methods when analysing specific groups in highly dynamic movements in order to increase the accuracy of the inverse dynamics analyses results

sloped muscle excitation waveforms improve the accuracy of forward dynamic simulations abstract mathematical models of the muscle excitation are useful in forward dynamic simulations of human movement tasks one objective was to demonstrate that sloped as opposed to rectangular excitation waveforms improve the accuracy of forward dynamic simulations a second objective was to demonstrate the differences in simulated muscle forces using sloped versus rectangular waveforms to fulfill these objectives surface emg signals from the triceps brachii and elbow joint angle were recorded and the intersegmental moment of the elbow joint was computed from 14 subjects who performed two cyclic elbow extension experiments at 200 and 300 deg s additionally the surface emg signals from the leg musculature joint angles and pedal forces were recorded and joint intersegmental moments were computed during a more complex pedaling task 90 rpm at 250 w using forward dynamic simulations four optimizations were performed in which the experimental intersegmental moment was tracked for the elbow extension tasks and four optimizations were performed in which the experimental pedal angle pedal forces and joint intersegmental moments were tracked for the pedaling task in these optimizations the three parameters onset and offset time and peak excitation defining the sloped triangular quadratic and hanning and rectangular excitation waveforms were varied to minimize the difference between the simulated and experimentally tracked quantities for the elbow extension task the intersegmental elbow moment root mean squared error onset timing error and offset timing error were less from simulations using a sloped excitation waveform compared to a rectangular excitation waveform p 0 001 the average and peak muscle forces were from 7 to 16 larger and 20 28 larger respectively when using a rectangular excitation waveform the tracking error for pedaling also decreased when using a sloped excitation waveform with the quadratic waveform generating the smallest tracking errors for both tasks these results support the use of sloped over rectangular excitation waveforms to establish greater confidence in the results of forward dynamic simulations

computation of invariant tori by the fourier methods in this paper we study systems of functional equations fes and first order partial differential equations pdes suggested in siam j sci statist comput 12 1991 pp 607 647 and siam j numer anal 29 1992 pp 1741 1768 as approximations for the computation of invariant tori the main new ideas of this paper are first to investigate these systems in the setting of hilbert spaces rather than in the setting of banach spaces and then to employ fourier methods instead of difference methods for a numerical solution based on the setting of sobolev spaces hs tp proper conditions for the pde and fe systems to be dissipative are described and some regularity results for the fe system are proved we studied two kinds of fourier methods the spectral method and the pseudospectral method in detail under dissipativity conditions convergence and optimal error estimates are shown theoretically for these fourier methods in the case of general linear systems numerical results for three examples provided in the last section indicate that the fourier method behaves very well not only for smooth solutions but also for nonsmooth solutions

certain classes of meromorphic multivalent functions in this paper we introduce and investigate two new classes of meromorphic multivalent functions such results as subordination properties coefficient inequalities convolution properties and integral representations are proved several sufficient conditions for meromorphic multivalent starlikeness and convexity are also derived

synergies in the ground reaction forces and moments during double support in curb negotiation in young and older adults abstract falls that occur while negotiating steps are a leading cause of death in older adults although recent efforts have improved understanding of the mechanics and control of stepping behaviors the double support phase during stepping is understudied therefore we quantified the stability of the resultant forces and moments acting on the body during this phase these quantities determine the movement of the body and therefore their stability is essential for successful stepping behavior we measured the ground reaction variables grvs under both feet as healthy young n 10 and older adults n 10 stepped up and down a curb we employed the uncontrolled manifold method to evaluate the hypotheses that the grvs covary to stabilize the resultant force and moment in the three coordinate directions robust stabilization of the resultant forces and moments was observed while stepping up however while stepping down the stability of the resultant moment was prioritized over that of the resultant forces in the vertical and the anterior posterior directions and the stability of the resultant medio lateral force was prioritized over that of the resultant anterior posterior force the salience of stabilizing whole body angular momentum and medio lateral motion during locomotion is well known but their prioritization during adaptive gait is a novel result and is possibly related to the higher likelihood of falling during descent versus ascent finally contrary to our expectations we observed no age differences in our stability indices indicating that healthy aging does not diminish the stability of the resultant forces and moments

subject specific regression equations to estimate lower spinal loads during symmetric and asymmetric static lifting abstract workplace safety assessment personalized treatment design and back pain prevention programs require accurate subject specific estimation of spinal loads since no noninvasive method can directly estimate spinal loads easy to use regression equations that are constructed based on the results of complex musculoskeletal models appear as viable alternatives thus we aim to develop subject specific regression equations of l4 l5 and l5 s1 shear and compression forces during various symmetric asymmetric tasks using a nonlinear personalized finite element musculoskeletal trunk model kinematics and electromyography emg activities of 19 young healthy subjects were collected during 64 different symmetric asymmetric tasks to investigate the reliability and accuracy of the musculoskeletal model and regression equations we compared estimated trunk muscle activities and l4 l5 intradiscal pressures idps respectively with our own electromyography data emgs and reported in vivo pressure measurements although in general six independent rotation components three trunk t11 rotations and three pelvic s1 rotations are required to determine kinematics along the spine only two surrogate variables trunk flexion and its asymmetric angles satisfactorily predicted all six rotation components r2 0 94 regression equations developed based on subject specific inputs predicted spinal loads in satisfactory agreement with idp measurements r2 0 85 predicted muscle activities in the personalized musculoskeletal models were in moderate to weak agreements with our measured emgs in 19 participants based on dominance analysis trunk flexion and its asymmetry angle hand load weight hand load lever arm and body weight were the most important variables while the effects of body height and sex on spinal loads remained small

generalization of treadmill perturbation to overground slip during gait effect of different perturbation distances on slip recovery treadmill perturbation training tm training may improve a person s fall resistance whereby adjusting slip distance can be a simple way to manipulate training intensity the purpose of this study was to determine the effects of different slip distances in tm training 12 cm vs 18 cm on its generalization to the recovery from a novel free slip during overground walking generalization here means the ability to apply learned skill from tm training to slip recovery during overground walking thirty six young adults in the tm 12 or the tm 18 group underwent either a 12 cm or an 18 cm slip during the treadmill walking for seven times or in the control group were not exposed to any perturbation their responses were also contrasted with previously reported results from overground perturbation training og training in which participants received either a 12 cm or an 18 cm slip during level walking with the same number of repetitions everyone was then exposed to the same generalization test during a novel free slip in overground walking their proactive and reactive control of stability was measured and compared tm training displayed a significant training effect in comparison to the control group p 0 05 these results underscore the further needs to investigate the potential of the treadmill as a convenient instrument that can effectively deliver perturbation training

body segment inertial parameter estimation for the general population of older adults the practical determination of accurate body segment inertial parameters for the general older adult population remains a problem especially in estimating these parameters for women and accounting for variations in body type a method is presented for determining the mass and center of mass location of the body segments of individuals within the general population of older adults effects of sex and body type on older adult mass distribution are accounted for using 32 easily obtainable body measurements the method is based on existing results from different data sources and employs a combination of validated estimation approaches including body mass and segment length proportions linear and nonlinear regression equations and a mathematical model of the trunk the method was applied to a validation sample of healthy community dwelling older adults 29 men 50 women predicted body mass was 96 7 4 8 and 95 7 3 7 of measured body mass in the men and women respectively the estimates of body segment mass and trunk center of mass location for the sample population approximate those reported in the literature supporting the validity of the described method by producing practical subject specific estimates of body segment inertial parameters the method should allow more accurate biomechanical analyses of the older adult population

breaststroke swimmers moderate internal work increases toward the highest stroke frequencies a model to predict the mechanical internal work of breaststroke swimming was designed it allowed us to explore the frequency internal work relationship in aquatic locomotion its accuracy was checked against internal work values calculated from kinematic sequences of eight participants swimming at three different self chosen paces model predictions closely matched experimental data 0 58 0 07 vs 0 59 0 05 j kg 1 m 1 t 23 0 30 p 0 77 which was reflected in a slope of the major axis regression between measured and predicted total internal work whose 95 confidence intervals included the value of 1 0 84 0 61 1 07 n 24 the model shed light on swimmers ability to moderate the increase in internal work at high stroke frequencies this strategy of energy minimization has never been observed before in humans but is present in quadrupedal and octopedal animal locomotion this was achieved through a reduced angular excursion of the heaviest segments 7 2 2 9 and 3 6 1 5 for the thighs and trunk respectively p 0 05 in favor of the lightest ones 8 8 2 3 and 7 4 1 0 for the shanks and forearms respectively p 0 05 a deeper understanding of the energy flow between the body segments and the environment is required to ascertain the possible dependency between internal and external work this will prove essential to better understand swimming mechanical cost determinants and power generation in aquatic movements

can stability really predict an impending slip related fall among older adults the primary purpose of this study was to systematically evaluate and compare the predictive power of falls for a battery of stability indices obtained during normal walking among community dwelling older adults one hundred and eighty seven community dwelling older adults participated in the study after walking regularly for 20 strides on a walkway participants were subjected to an unannounced slip during gait under the protection of a safety harness full body kinematics and kinetics were monitored during walking using a motion capture system synchronized with force plates stability variables including feasible stability region measurement margin of stability the maximum floquet multiplier the lyapunov exponents short and long term and the variability of gait parameters including the step length step width and step time were calculated for each subject sensitivity of predicting slip outcome fall vs recovery was examined for each stability variable using logistic regression results showed that the feasible stability region measurement predicted fall incidence among these subjects with the highest sensitivity 68 4 except for the step width with an sensitivity of 60 2 no other stability variables could differentiate fallers from those who did not fall for the sample included in this study the findings from the present study could provide guidance to identify individuals at increased risk of falling using the feasible stability region measurement or variability of the step width

on integral operators abstract let fn z z 1 z n 1 n no and f 1 n be defined such that f n f 1 n z 1 z where denotes convolution hadamard product let f be analytic in the unit disc e we define a new operator inf f 1 n f which is analogous to one defined by ruscheweyh using this operator the classes m n are defined a function f analytic in e is in m n if and only if inf is close to convex the properties of f m n are discussed in some detail it is shown that m n m n 1 for n no and for n 0 1 m n consists entirely of univalent functions closure properties of some integral operators defined on m n are also given

mechanical demand and multijoint control during landing depend on orientation of the body segments relative to the reaction force the purpose of this study was to determine how diverse momentum conditions and anatomical orientation at contact influences mechanical loading and multijoint control of the reaction force during landings male collegiate gymnasts n 6 performed competition style landings n 3 of drop jumps front saltos and back saltos from a platform 0 72 m onto landing mats 0 12 m kinematics 200 fps reaction forces 800 hz and muscle activation patterns surface emg 1600 hz of seven lower extremity muscles were collected simultaneously between task differences in segment orientation relative to the reaction force contributed to significant between task differences in knee and hip net joint moments njm during the impact phase during the stabilization phase ankle knee and hip njms acted to control joint flexion between task differences in muscle activation patterns indicated that gymnasts scaled biarticular muscle activation to accommodate for between task differences in njm after contact activation of muscles on both sides of the joint suggests that impedance like control was used to stabilize the joints and satisfy the mechanical demand imposed on the lower extremity between subject differences in the set of muscles used to control total body center of mass tbcm trajectory and achieve lower extremity njms suggests that control of multijoint movements involving impact needs to incorporate mechanical objectives at both the total body and local level the functional consequences of such a control structure may prove to be an asset to gymnasts particularly when required to perform a variety of landing tasks under a variety of environmental constraints

adjustments to mcconville et al and young et al body segment inertial parameters body segment inertial parameters bsips are important data in biomechanics they are usually estimated from predictive equations reported in the literature however most of the predictive equations are ambiguously applicable in the conventional 3d segment coordinate systems scss also the predictive equations reported in the literature all include two assumptions the centre of mass and the proximal and distal endpoints are assumed to be aligned and the inertia tensor is assumed to be principal in the segment axes these predictive equations restraining both position of the centre of mass and orientation of the principal axes of inertia become restrictive when computing 3d inverse dynamics when analyzing the influence of bsip estimations on joint forces and moments and when evaluating personalized 3d bsips obtained from medical imaging in the current study the extensive data from mcconville et al 1980 anthropometric relationships of body and body segment moments of inertia afamrl tr 80 119 aerospace medical research laboratory wright patterson air force base dayton ohio and from young et al 1983 anthropometric and mass distribution characteristics of the adults female technical report afamrl tr 80 119 faa civil aeromedical institute oklaoma city oklaoma are adjusted in order to correspond to joint centres and to conventional segment axes in this way scaling equations are obtained for both males and females that provide bsips which are directly applicable in the conventional scss and do not restrain the position of the centre of mass and the orientation of the principal axes these adjusted scaling equations may be useful for researchers who wish to use appropriate 3d bsips for posture and movement analysis

segment interaction analysis of the stance limb in sprint running a high angular velocity of the thigh of the stance limb generated by hip extensor musculature is commonly thought to be a performance determining factor in sprint running however the thigh segment is a component of a linked system i e the lower limb therefore it is unlikely that the kinematics of the thigh will be due exclusively to the resultant joint moment rjm at the hip the purpose of this study was to quantify by means of segment interaction analysis the determinants of sagittal plane kinematics of the lower limb segments during the stance phase of sprint running video and ground reaction force data were collected from four male athletes performing maximal effort sprints the analysis revealed that during the first third of the stance phase a hip extension moment was the major determinant of the increasing angular velocity of the thigh however during the mid third of stance hip and knee extension moments and segment interaction effects all contributed to the thigh attaining its peak angular velocity extension moments at the ankle and to a lesser extent the knee were attributed with preventing the collapse of the shank under the effects of the interactive moment due to ground reaction force the angular acceleration of the foot was determined almost completely by the rjm at the ankle and the interactive moment due to ground reaction force further research is required to determine if similar results exit for a wide range of athletes and for other stages of a sprint race e g early acceleration maximal velocity and deceleration phases

body segment inertial parameters and low back load in individuals with central adiposity abstract there is a paucity of information regarding the impact of central adiposity on the inertial characteristics of body segments deriving low back loads during lifting requires accurate estimate of inertial parameters the purpose was to determine the body segment inertial parameters of people with central adiposity using a photogrammetric technique and then to evaluate the impact on lumbar spine loading five participants with central adiposity waist hip ratio 0 9 waist circumference 102 cm were compared to a normal bmi group a 3d wireframe model of the surface topography was constructed partitioned into 8 body segments and then body segment inertial parameters were calculated using volumetric integration assuming uniform segment densities for the segments central adiposity dependent increases in body segment parameters ranged from 12 to 400 varying across segments greatest for trunk and parameters the increase in mass distribution to the trunk was accompanied by an anterior and inferior shift of the centre of mass a proximal shift in centre of mass was detected for the extremities along with a reduction in mass distribution to the lower extremity l5 s1 torques 392 vs 263 nm and compressive forces 5918 vs 3986 n were substantially elevated in comparison to the normal bmi group as well as in comparison to torques and forces predicted using published bsip equations central adiposity resulted in substantial but non uniform increases in inertial parameters resulting in task specific increases in torque and compressive loads arising from different inertial and physical components

a novel approach to study human posture control principal movements obtained from a principal component analysis of kinematic marker data human upright posture is maintained by postural movements which can be quantified by principal movements pms obtained through a principal component analysis pca of kinematic marker data the current study expands the concept of principal movements in analogy to newton s mechanics by defining principal position pp principal velocity pv and principal acceleration pa and demonstrates that a linear combination of pps and pas determines the center of pressure cop variance in upright standing twenty one subjects equipped with 27 markers distributed over all body segments stood on a force plate while their postural movements were recorded using a standard motion tracking system a pca calculated on normalized and weighted posture vectors yielded the pps and their time derivatives the pvs and pas cop variance explained by the pps and pas was obtained through a regression analysis the first 15 pms quantified 99 3 of the postural variance and explained 99 60 0 22 mean sd of the anterior posterior and 98 82 0 74 of the lateral cop variance in the 21 subjects calculation of the pms thus provides a data driven definition of variables that simultaneously quantify the state of the postural system pps and pvs and the activity of the neuro muscular controller pas since the definition of pps and pas is consistent with newton s mechanics these variables facilitate studying how mechanical variables such as the cop motion are governed by the postural control system

some subclasses of meromorphically multivalent functions associated with the generalized hypergeometric function in the present paper we introduce and investigate each of the following new subclasses f p k q s a a 1 f g p q s a a 1 f andh p q s a a 1 f as well as f p k q s a a 1 f g p q s a a 1 f andh p q s a a 1 f of meromorphically p valent functions which is defined by means of a certain meromorphically p modified version of the familiar dziok srivastava linear operator involving the generalized hypergeometric function such results as inclusion relationships integral representations and convolution properties for these function classes are proved the results presented here provide extensions of those given in some earlier works several other new results are also obtained

on the concept of attractor this note proposes a definition for the concept of attractor based on the probable asymptotic behavior of orbits the definition is sufficiently broad so that every smooth compact dynamical system has at least one attractor

non driving intersegmental knee moments in cycling computed using a model that includes three dimensional kinematics of the shank foot and the effect of simplifying assumptions assessing the importance of non driving intersegmental knee moments i e varus valgus and internal external axial moments on over use knee injuries in cycling requires the use of a three dimensional 3 d model to compute these loads the objectives of this study were 1 to develop a complete 3 d model of the lower limb to calculate the 3 d knee loads during pedaling for a sample of the competitive cycling population and 2 to examine the effects of simplifying assumptions on the calculations of the non driving knee moments the non driving knee moments were computed using a complete 3 d model that allowed three rotational degrees of freedom at the knee joint included the 3 d inertial loads of the shank foot and computed knee loads in a shank fixed coordinate system all input data which included the 3 d segment kinematics and the six pedal load components were collected from the right limb of 15 competitive cyclists while pedaling at 225 w and 90 rpm on average the peak varus and internal axial moments of 7 8 and 1 5 n m respectively occurred during the power stroke whereas the peak valgus and external axial moments of 8 1 and 2 5 n m respectively occurred during the recovery stroke however the non driving knee moments were highly variable between subjects the coefficients of variability in the peak values ranged from 38 7 to 72 6 when it was assumed that the inertial loads of the shank foot for motion out of the sagittal plane were zero the root mean squared difference rmsd in the non driving knee moments relative to those for the complete model was 12 of the peak varus valgus moment and 25 of the peak axial moment when it was also assumed that the knee joint was revolute with the flexion extension axis perpendicular to the sagittal plane the rmsd increased to 24 of the peak varus valgus moment and 204 of the peak axial moment thus the 3 d orientation of the shank segment has a major affect on the computation of the non driving knee moments while the inertial contributions to these loads for motions out of the sagittal plane are less important

computation of trunk equilibrium and stability in free flexion extension movements at different velocities velocity of movement has been suggested as a risk factor for low back disorders the effect of changes in velocity during unconstrained flexion extension movements on muscle activations spinal loads base reaction forces and system stability was computed in vivo measurements of kinematics and ground reaction forces were initially carried out on young asymptomatic subjects the collected kinematics of three subjects representing maximum mean and minimum lumbar rotations were subsequently used in the kinematics driven model to compute results during the entire movements at three different velocities estimated spinal loads and muscle forces were significantly larger in fastest pace as compared to slower ones indicating the effect of inertial forces spinal stability was improved in larger trunk flexion angles and fastest movement partial or full flexion relaxation of global extensor muscles occurred only in slower movements some local lumbar muscles especially in subjects with larger lumbar flexion and at slower paces also demonstrated flexion relaxation results confirmed the crucial role of movement velocity on spinal biomechanics predictions also demonstrated the important role on response of the magnitude of peak lumbar rotation and its temporal variation

predicted threshold against backward balance loss following a slip in gait the purpose of this study was to use a 7 link moment actuated human model to predict at liftoff of the trailing foot in gait the threshold of the center of mass com velocity relative to the base of support bos required to prevent backward balance loss during single stance recovery from a slip five dynamic optimization problems were solved to find the minimum com velocities that would allow the simulation to terminate with the com above the bos when the com started 0 25 0 5 0 75 1 0 and 1 25 foot lengths behind the heel of the stance foot i e behind the bos the initial joint angles of the model were based on averaged data from experimental trials foot ground contact was modeled using 16 visco elastic springs distributed under the stance foot slipping was modeled by setting the sliding coefficient of friction of these springs to 0 02 the forward velocity of the com necessary to avoid a backward balance loss is nearly two times larger under slip conditions under non slip conditions the predicted threshold for backward balance loss following a slip agreed well with experimental data collected from 99 young adults in response to 927 slips during walking in all trials in which a subject s com had a velocity below the predicted threshold the subject s recovery foot landed posterior to the slipping foot as predicted finally combining experimental data with optimization we verified that the 7 link model could more accurately predict gait stability than a 2 link model

a system to measure the kinematics during the entire ski jump sequence using inertial sensors three dimensional analysis of the entire sequence in ski jumping is recommended when studying the kinematics or evaluating performance camera based systems which allow three dimensional kinematics measurement are complex to set up and require extensive post processing usually limiting ski jumping analyses to small numbers of jumps in this study a simple method using a wearable inertial sensors based system is described to measure the orientation of the lower body segments sacrum thighs shanks and skis during the entire jump sequence this new method combines the fusion of inertial signals and biomechanical constraints of ski jumping its performance was evaluated in terms of validity and sensitivity to different performances based on 22 athletes monitored during daily training the validity of the method was assessed by comparing the inclination of the ski and the slope at landing point and reported an error of 0 2 4 8 the validity was also assessed by comparison of characteristic angles obtained with the proposed system and reference values in the literature the differences were smaller than 6 for 75 of the angles and smaller than 15 for 90 of the angles the sensitivity to different performances was evaluated by comparing the angles between two groups of athletes with different jump lengths and by assessing the association between angles and jump lengths the differences of technique observed between athletes and the associations with jumps length agreed with the literature in conclusion these results suggest that this system is a promising tool for a generalization of three dimensional kinematics analysis in ski jumping

computation of trunk stability in forward perturbations effects of preload perturbation load initial flexion and abdominal preactivation spine stability demand influences active passive coordination of the trunk response especially during sudden perturbations the objective of this study was to look at the role of passive stationary active and reflexive subsystems on spinal stability spine stability was evaluated here during pre and post perturbation phases by computing the minimum i e critical muscle stiffness coefficient required to maintain stability the effects of pre perturbation conditions preloading initial posture and abdominal antagonistic coactivation as well as perturbation magnitude were studied results revealed that higher preload initially flexed trunk posture and abdominal pre activation enhanced pre perturbation stiffness and stability in contrast to the preload however larger sudden load initial flexion and abdominal preactivation significantly increased post perturbation stability margin as a result much lower critical muscle stiffness coefficient was required post perturbation compared to the pre perturbation phase the trunk stiffness and stability substantially increased post perturbation demanding thus a much lower critical muscle stiffness coefficient overall these findings highlight the crucial role of the ligamentous spine and muscles in both passive and active states in augmenting the trunk stiffness and hence stability during pre and post perturbation phases a role much evident in the presence of initial trunk flexion