Abstract: The frictional collision of multi-rigid-body systems is studied. General normal elastic-plastic force-displacement relationship is directly introduced in the calculation of multi-rigid-body systems, and slip-stick and slip?- at the contact point are considered. In existing literatures, the differential method is often used to solve this problem. But due to the much shorter collision time and the much larger force, the choice of calculating step becomes very difficult. Moreover, the non?smoothness of Amontons-Coulomb frictional law leads to the difficulties in finding non?smooth point between sticking and sliding states. Instead of returning to the calculation of differential equation, algebraic method to calculate the states after collision is applied. By the bridge of energetic coefficient of restitution and keeping the traditional approximate assumptions of impact, the dynamic state after the collision can be obtained according to initial conditions before the impact and geometry properties of the system, which energetic coefficient of restitution is calculated as a function of initial conditions based on general normal contact deformation law instead of a material property. The method avoids energy inconsistency and is much more simple.

Key words: frictional collision, multi-rigid-body systems, energetic coefficient of restitution

摘要： 研究了多刚体系统的摩擦碰撞问题。一般的法向弹塑性力与位移的关系被直接引入到多刚体系统的计算中，同时考虑了碰撞中滑动模式的变化。在现存的文献中，常通过求解微分方程来解决该问题，但因碰撞时间同碰撞力不在同一个量级上，这就导致计算步长的选择十分困难，而且Amontons-Coulomb摩擦定律的不光滑性导致了在搜索粘滞状态与滑动状态的非光滑点的困难。代替通常的解微分方程的方法，以能量恢复系数作为桥梁，通过代数的方法得到碰撞前后系统状态。其主要优点在于既避免了能量的不协调性，又比微分方法简单。

关键词: 摩擦碰撞, 多刚体系统, 能量恢复系数