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.