树形多体Hamilton系统的Lyapunov指数计算方法

Numerical Algorithm for Calculating Lyapunov Exponents of Multibody Hamilton Systems with Topological Tree Configuration

研究了树形多体Hamilton系统Lyapunov指数的数值方法 .利用多体Hamilton系统的正则方程和辛算法 ,给出了多体Hamilton系统Lyapunov指数的计算方法 ,该算法具有较好的计算精度和通用性 .利用该算法可对系统的运动稳定性进行分析 .最后用算例说明了该算法的有效性 .

A numerical algorithm for calculating Lyapunov exponents of Hamiltonian multibody systems with topological tree configuration is studied. The algorithms for Lyapunov exponents of Hamiltonian multibody systems using the canonical equations of the system and symplectic algorithm for ordinary differential equations are presented, which are used to study the stability of the Hamiltonian multibody systems. An example is given to analyze the stability of a typical Hamiltonian multibody system, including periodic solution and chaos.