中文摘要：

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.

英文摘要：

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.