Inelastic collisions of three particles on a line as a two-dimensional billiard. (English) Zbl 0900.70198

Summary: 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 \(r\leq r_c\), 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 \(r\).


70F35 Collision of rigid or pseudo-rigid bodies
Full Text: DOI


[1] Bernu, B.; Mazighi, R., J. phys. A, 23, 5745, (1990) · Zbl 0729.73648
[2] MacNamara, S.; Young, W.R., Phys. fluids A, 4, 496, (1992)
[3] Goldhirsch, I.; Zanetti, G., Phys. rev. lett., 70, 1619, (1993)
[4] S. MacNamara and W.R. Young, preprint 1994 (unpublished).
[5] Kozlov, V.V.; Treshchev, D.V., Billiards: A genetic introduction to the dynamics of systems with impacts, (1991), American Mathematical Society Providence, Rhode Island · Zbl 0751.70009
[6] Clement, E.; Luding, S.; Blumen, A.; Rajchenbach, J.; Duran, J., Int. J. mod. phys. B, 7, 1807, (1993)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.