非光滑多体系统最大Lyapunov指数的计算方法

富立; 王琪

非光滑多体系统最大Lyapunov指数的计算方法

富立,
王琪

北京航空航天大学航空科学与工程学院, 北京 100191

基金项目: 国家自然科学基金资助项目(10672007)

详细信息

中图分类号: O 313.7
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出版历程
- 收稿日期: 2009-11-26
- 网络出版日期: 2011-01-31

Method for estimating largest Lyapunov exponent in non-smooth multibody systems

Fu Li,
Wang Qi

School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

摘要

摘要: 结合非光滑力学与非线性动力学的理论给出非光滑多体系统最大Lyapunov指数的数值计算方法.应用第一类Lagrange方法建立具有单边约束非光滑多体系统变拓扑结构动力学方程;应用线性互补理论与方法检测非光滑事件;应用混沌同步方法计算Lyapunov指数.在提高计算速度方面,提出了采用二分搜索法加快搜索速度以及采用调制参数方法加快系统达到同步状态的速度.通过算例说明本文算法的可行性与有效性.
- 非光滑 /
- 多体系统 /
- 线性互补问题 /
- 混沌同步 /
- Lyapunov指数
Abstract: According to the theories of both non-smooth mechanics and non-linear dynamics, a numerical method for estimating the largest Lyapunov exponent in non-smooth multi-body systems with unilateral constraints was presented. Lagrange equation of the first kind was applied to derive the structure-varying dynamic equations of the systems and the scheme for linear complementarity problem(LCP) was used to detect non-smooth events, such as stick-slip transition, detachment,collision andsoon.Chaos synchronization method was applied to estimate the largest Lyapunov exponent. The algorithm of bisection and the algorithm of coupling parameter modulation were used to increase the speed of calculation.The numerical results obtained from two examples indicate that the method is effective.
- non-smooth /
- multibody system /
- linear complementarity problem /
- chaos synchronization /
- Lyapunov exponent

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参考文献(1)

[1] De Souza S L T,Caldas I L.Calculation of Lyapunov exponents in systems with impacts[J].Chaos,Solitons and Fractals,2004,19(3):569-579 [2] Jin L,Lu Q S,Twizell E H.A method for calculating the spectrum of Lyapunov exponents by local maps in non-smooth impact-vibrating systems[J].Journal of Sound and Vibration,2006,298(4/5):1019-1033 [3] Andrzej Stefanski,Tomasz Kapitaniak.Using chaos synchronization to estimate the largest Lyapunov exponent of non-smooth systems [J].Discrete Dynamics in Natural & Society,2000,4:207-215 [4] 王琪,黄克累,陆启韶.树形多体系统非线性动力学的数值分析方法[J].固体力学学报,1999,20(4):363-367 Wang Qi,Huang Kelei,Lu Qishao.A numerical algorithm for nonlinear dynamical analysis of multibody systems with topological tree configuration[J].Acta Mechanica Solida Sinica,1999,20(4):363-367 (in Chinese) [5] 金俐,王琪,陆启韶.树形多体Hamilton 系统的Lyapunov 指数计算方法[J].北京航空航天大学学报,2001,27(2):230-232 Jin Li,Wang Qi,Lu Qishao.A method for calculating the Lyapunov exponents in tree binding multibody Hamiltonian systems[J].Journal of Beijing University of Aeronautics and Astronautics,2001,27(2):230-232(in Chinese) [6] Fu Shihui,Wang Qi.Estimating the largest Lyapunov exponent in a multibody system with dry friction by using chaos synchromization[J].Acta Mechanica Sinica,2006,22(3):277-283 [7] Stefariski A,Kapitaniak T.Estimation of the dominant Lyapunov exponent of non-smooth systems on the basis of maps synchronization[J].Chaos,Solitons and Fractals,2003,15(2):233-244 [8] Pfeiffer F.On non-smooth dynamics[J].Meccanica,2008,4(5):533-554 [9] Fu Li,Wang Qi,Wang Shimin.Time-stepping for multibody dynamics with friction-affected bilateral constraints[J].Progress in Natrual Science,2009,19(12),1799-1804 [10] Leine R I,Van Campen D H,Van De Vrande B L.Bifurcations in nonlinear discontinuous systems[J].Nonlinear Dynamics,2000,23(2):105-164

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