Theoretical Analysis of Multiple Impact of Three Balls System

An effective theoretical method is developed to analyze three-ball system at contact in a bidimensional case basing on the impact law. The accurate solutions of the post-velocity have been computed in the paper. With the increase of between BallII and Ball III, the post-velocity of Ball III will be less and less. In fact, in the case of , the three-ball system in the same plane is consistent with the three-ball system in co-linear, when , the impact is happened only between BallI and Ball II. It is proved that the vibrating frequency influences only the impact time and the displacement of each ball for the three-ball system in the plane with elastic impact, but can not affect the momentum transfer and the post-velocities of the three balls, and all possible rigid solutions for impact are the limits of the theoretical results in some parameters of the system actually.