在速度空间中研究两个小球的一维自由碰撞问题，可以直接发现质心系是一个特殊的惯性参照系，碰撞引起的最大可能的动能损耗就是在此质心系中两个小球的全部动能( 对应完全非弹性碰撞) ，而一般非弹性碰撞的动能损耗只是此全部动能的一部分，其比例系数与牛顿恢复系数( 碰撞前后的相对速度之比) 有关.研究表明，小球一维自由碰撞的概念可以扩充到与刚体的碰撞，碰撞等效折合质量的倒数等于诸参与碰撞物体的特征参量的倒数之和; 由分离速度除以接近速度得到的牛顿恢复系数公式是普遍成立的，其中分离速度和接近速度都是指两物体上碰撞点的速度; 小球的二维碰撞可以通过一个主要碰撞( 相对速度过零) 和一个与它正交的伴随碰撞( 相对速度不过零) 的复合过程表示出来.

Studying one-dimensional free collision of two small balls in the velocity space can directly find that the centroid system is a special inertial reference system.The most possible kinetic energy loss caused by collision is the total kinetic energy of two small balls in this centroid system ( corresponding to completely inelastic collision) . The kinetic energy loss of general inelastic collision is only a part of the total kinetic energy，and its proportional coefficient. It is related to Newton's coefficient of recovery ( the ratio of relative velocity before and after collision) .The results show that the concept of one-dimensional free collision of a sphere can be extended to the collision with a rigid body，and the reciprocal of the equivalent reduced mass of the collision is equal to the sum of the reciprocal of the characteristic parameters of the objects involved in the collision. The Newton recovery coefficient formula obtained by dividing the separation velocity by the approaching velocity is generally valid， in which the separation velocity and the approaching velocity refer to the velocity of the collision points on two objects.Two-dimensional collisions can be represented by a composite process of a major collision ( relative velocity zero crossing) and an adjoin collision ( relative velocity no more than zero) orthogonal to it.