Abstract: The purpose is to study the solution of impulsive dynamics of planar discrete system with friction and multiple-point impact. When impact applies on a discrete system in which one of constraints is a constant with coulomb friction, the phenomenon of slip-stick at the point can cause the change of friction and the integration for frictional force during infinitesimal impulsive interval becomes impossible according to traditional impulsive dynamics of discrete systems. By introducing a new dimensional time parameter, first-order momentum-impulse differential equations are obtained and the discussion over infinitesimal impulsive interval is transformed into a piece-wise study on the finite region of impulse. An algorithm for response of impact and an example are given.

Key words: friction, multiple-point impact, discrete system, piece-wise, impact dynamics

摘要： 研究受到多个打击的离散系统考虑库仑摩擦时动力学的求解方法。当离散系统受到冲击时，若约束为非理想时，摩擦作用点的滑动速度的变化及黏滞现象会带来相应的摩擦力方向的变化，所以按照经典的离散系统的冲击动力学的方法无法处理在无限小的冲击时间内摩擦力的积分问题。在引入新的无量纲的时间参数后，通过建立相应的动量-冲量的一阶微分方程，在趋近于零的冲击区间的讨论变为在有限区间中来分段研究含滑动-黏滞的冲击过程，得到了受到多点打击的离散系统考虑库仑摩擦时的动力学的求解方法，即根据冲击前的初始状态无需回到繁琐的微分方程的求解便可以得到冲击后系统的动力学响应。给出了计算流程及算例。

关键词: 摩擦, 多点打击, 离散系统, 分段, 冲击动力学