Abstract: 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.

Key words: collision, restitution coefficient, centroid system, reduced mass, relative velocity