具有摩擦的刚体碰撞

刚体碰撞是力学上的一个经典问题，但目前大都采用给定恢复系数进行分析的方法，本文则直接从两刚体碰撞时Newton第二定律出发，建立了计及摩擦的两刚体碰撞基本理论，并指出了以往研究通过给定恢复系数方法的错误之处。文中通过利用两刚体接触相对变位加速度与碰撞力的关系，定义了法向等效质量，对二维平面碰撞，通过一些简单的比较和定义给出了各种碰撞状态的分类判别法，并给出了碰撞力和冲量的解析式。指出法向等效质量依赖于碰撞状态，在反向滑动和停止滑动这两状态下的法向等效质量是变化的，因此导致其恢复系数是变化的，这样，恢复系数不仅与接触力(接触点情况)有关，而且还与两刚体的运动和动力参数有关，同时给出各种碰撞状态下的恢复系数计算式。

Rigid-Body Collisions with Friction

The collisions of rigid bodies is a classical problem, however, the coefficient of restitution is used in the conventional researches to study this problem. The authors present a new way for this kind of problem. A theory of the collision between two rigid bodies in two dimensions, taking account of friction, is proposed according the Newton first law. And the shortages of former researchers are justified. Using the relation between the impulsive force and acceleration in normal directions, the equivalent mass in normal direction is defined. A classification method for collision states is presented using a few simple comparisons and some definitions, and analytical expressions for impulsive force and impulse are derived. Results show that the equivalent mass in normal direction depends on the modes of collision. In the case of reversed sliding and sticking, the coefficient of restitution varies as a result of the instantaneously changes of the equivalent mass during impacting process. The coefficient of restitution depends not only on the contact force, but also on the kinematical and dynamic parameters of the two rigid bodies. Moreover, a formula is proposed to calculate the coefficient of restitution.