带约束多体系统Lyapunov指数的数值计算方法

付士慧; 王琪

带约束多体系统Lyapunov指数的数值计算方法

付士慧,
王琪

北京航空航天大学理学院, 北京 100083

基金项目: 国家自然科学基金资助项目(10272008)

详细信息

作者简介:
付士慧(1977-), 女, 河北保定人, 博士生,fshtp@163.com.

中图分类号: O 316
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- 被引次数: 0
出版历程
- 收稿日期: 2005-06-17
- 网络出版日期: 2006-06-30

Numerical method for Lyapunov exponents of multibody systems with constraints

Fu Shihui,
Wang Qi

School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, China

摘要

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.
- 多体系统 /
- 微分-代数方程 /
- Lagrange方程 /
- Lyapunov指数
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.
- multibody system /
- differential-algebraic equation /
- Lagrange equation /
- Lyapunov exponent

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参考文献(1)

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