Numerical Algorithm for Calculating Lyapunov Exponents of Multibody Hamilton Systems with Topological Tree Configuration
-
摘要: 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.
-
关键词:
- 哈密顿方程 /
- 辛结构 /
- 计算方法 /
- 多体系统 /
- Lyapunov指数
Abstract: 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. -
[1] Kovacs A P, Ibrahim R A. Relationship between multibody dynamics computation and nonlinear vibration theory[J]. Nonlinear Dynamics, 1993, 4(3):634~653. [2] 王 琪,陆启韶,黄克累. 树形多体系统动力学的隐式数值方法[J]．力学学报,1996,28(6):717~725． [3] 王 琪,陆启韶,黄克累. 树形多体Hamilton系统辛算法[J]．计算物理,1997,14(1):35~39． [4] Thomas S Parker, Leon O Chua. Practical numerical algorithms for chaotic systems[M]. New York:Springer-Verlag,1990． [5] 秦孟兆．辛几何及计算哈密顿力学[J]．力学与实践,1990,12(6):1~20． [6] Touati D, Cederbaum G． Influence of large deflections on the dynamic stability of nonlinear viscoelastic plates[J]． Acta Mechanica, 1995, 113:215~231． -
点击查看大图
计量
- 文章访问数: 2687
- HTML全文浏览量: 79
- PDF下载量: 1239
- 被引次数: 0
下载:
