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.
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
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
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:-
����,�ƿ���,½����.���ζ���ϵͳ�����Զ���ѧ����ֵ��������[J].������ѧѧ��,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)