Collision of four balls aligned

Abstract

The collision of four balls aligned is analyzed in this paper. This study is based on the fundamental idea that a system formed by rigid bodies is deformable, since its shape changes because the relative distances of the different bodies change. A simple linear constitutive law, described by a pseudo-potential of dissipation completed by the condition of the impenetrability between the balls, is used. we consider the case where three balls falls on a very massive obstacle. The first ball, considered of very light mass, bounces with a velocity extensively superior to its fall velocity. This is sometimes called the superball phenomenon. This phenomenon is produced according to different cases such as the interaction between the first ball and the massive obstacle must be presented. Introducing an interaction between the first ball and the massive obstacle through the second or the third ball, the superball phenomenon is produced for all cases of evolutions after the collision. For every cases of evolutions of the balls after the collision, has been investigated the relations on the physical parameters which insure the superball phenomenon. These relations are obtained on the basis of the fundamental hypothesis: the mass of the first ball is very small whereas the mass of the massive obstacle is very large.