带干摩擦的非光滑动力系统Lyapunov指数的数值计算  

NUMERICAL CALCULATION OF LYAPUNOV EXPONENTS OF DISCONTIMUOUS SYSTEMS WITH DRY FRICTION

作　　者：付士慧[1] 王琪[1] 王士敏[1] 

机构地区：[1]北京航空航天大学理学院,北京100083

出　　处：《动力学与控制学报》2006年第3期210-216,共7页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(10272008)~~

摘　　要：对带干摩擦的非光滑动力系统,在不连续点利用闭上链(cocycle)得到一个传递矩阵,由此给出一种非光滑动力系统Lyapunov指数的数值计算方法.该方法是根据计算光滑动力系统Lyapunov指数的数值方法而提出的.通过对带干摩擦的动力系统进行Lyapunov指数的数值计算,结合时间历程图和Poincare映射对其动力学特性进行了分析.数值结果表明该方法的可行性和有效性,与一般的计算非光滑动力系统Lyapunov指数的数值算法相比,该方法更便于数值计算.For nonsmooth systems with dry friction, the transitional matrix was deduced from the cocycle at the nonsmooth instants, and then a numerical method for calculating Lyapunov exponents was introduced by means of the transitional matrix. The method was conducted from conventional algorithm of calculating Lyapunov exponents for smooth systems. The dynamical behavior of a system with dry friction was analyzed by calculating its Lyapunov exponents, along with time history and Poincare map; and numerical results showed the effectiveness of the method. Compared with some existent methods of calculating Lyapunov exponents of nonsmooth systems, the method is more adequate to numerical calculation.

关 键 词：干摩擦 传递矩阵 非光滑动力系统 LYAPUNOV指数 

分 类 号：O19[理学—数学]