【摘要】 研究了树形多体系统非线性动力学分析的数值方法.利用多体系统的正则方程及其线性化方程,给出了多体系统Lyapunov 指数和Poincare 映射的计算方法,该算法具有较好的计算精度和通用性,既适用于自治系统也适用于非自治系统.利用该算法可对多体系统的动力学行为进行分析.最后用算例说明该算法的有效性,并对该系统的动力学特性( 周期解、准周期解、分岔、混沌以及通往混沌的道路等)进行了分析更多还原

【Abstract】 A numerical algorithm for nonlinear dynamical analysis of multibody systems with topological tree configuration is studied. The canonical equations and linearized equations of the system both are obtained in the form of matrix. The paper presents the algorithms for Lyapunov exponents and Poincare map of autonomous and non autonomous multibody systems, which are used to study dynamical behaviour of the multibody systems. An example is taken to analyze the dynamical behaviour of a typical multibody system, including periodic solution, quasi periodic solution, bifurcation and chaos.更多还原