Modeling of rebound phenomenon of a rigid ball with friction and elastic effects

We derive analytical models of the rebound phenomenon between a ping-pong ball and the table/racket rubber. In the rebound model of the table, the determination of the type of the contact during the impact is derived as a generalized condition in the 3-dimensional space. In the model between the ball and racket rubber, it is assumed that the kinetic energy of the tangent velocity is stored as the potential energy due to the elasticity of the rubber. This assumption leads to that the impulse in the horizontal direction is proportional to the tangent velocity. The models are verified by experimental data.