# Collision of four balls aligned

## 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. | Vietnam Journal of Mechanics, VAST, Vol. 32, No. 3 (2010), pp. 145 – 156 COLLISION OF FOUR BALLS ALIGNED Othman Ben Mekki1 and Michel Frémond2 1 Università di Roma "Tor Vergata", Italy 2 Laboratoire Central des Ponts et Chausses, France 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. 1. INTRODUCTION Let us consider a heavy ball with mass m3 on which rest two other balls with masses m2 and m1 . These balls fall on a very massive obstacle with mass m4 , Fig. 1. Mass m1 is assumed to be very small. Experiments show that when the three balls collide the very massive obstacle, ball 1 rebounds with a very large upward velocity. We intend to give a predictive theory accounting for this spectacular .

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