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

Constantin, Peter; Grossman, Elizabeth; Mungan, Muhittin

Physica D 83, No. 4, 409-420 (1995).

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 \(r\).

MSC:

70F35

Collision of rigid or pseudo-rigid bodies

Keywords:

unconvential reflection laws; asymptotic behavior; coefficient of restitution; convential billiard in infinite wedge; triple collisions

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