【摘要】 应用第1类Lagrange方程建立的带约束多体系统动力学方程为非线性微分-代数方程组.利用增广法,将其转化成了常微分方程组,并表示成矩阵形式.根据方程的特点,给出了方程的Jacobi矩阵的具体表达式,提高了计算效率.在此基础上,给出了Lyapunov指数的数值计算方法,并通过对具体的树形和非树形多体系统进行Lyapunov指数数值计算,结合相图和Poincare映射对系统的动力学特性进行了分析,表明了该方法的可行性和有效性.更多还原

【Abstract】 Dynamic equations of multibody systems with constraints induced by the first kind of Lagrange’s equations are nonlinear differential-algebraic equations.To be solved numerically,nonlinear differential-algebraic equations were transformed into ordinary differential equations with the augmentation approach.Ordinary differential equations and their Jacobian matrix were given in the matrix form to improve computational efficiency.A numerical method of Lyapunov exponents of nonlinear dynamics of multibody systems was demonstrated.An example was given to analysis dynamical behavior of two multibody systems with topological tree and non-tree configuration,such as bifurcation and chaos by calculating Lyapunov exponents along with Poincare maps and phase graphs.更多还原