INELASTIC-COLLISIONS OF 3 PARTICLES ON A LINE AS A 2-DIMENSIONAL BILLIARD

We study the inelastic collisions of three particles on a line, We show that this system is a two dimensional billiard in a semi-enclosed space with unconventional reflection laws, Using this geometric language, we describe completely the dynamics of this system. We find that the asymptotic behavior changes when the coefficient of restitution becomes smaller than a critical value r(c). For r > r(c), the system can be understood in terms of a conventional billiard in an infinite wedge. For r less than or equal to r(c), this is no longer true and the asymptotic behavior is richer. We also investigate the question of triple collisions and find that they are regularizable only for certain values of r.