Inelastic collisions of three particles on a line as a two-dimensional billiard

Peter Constantin; Elizabeth Grossman; Muhittin Mungan

doi:10.1016/0167-2789(95)00042-3

Inelastic collisions of three particles on a line as a two-dimensional billiard

Peter Constantin, Elizabeth Grossman, Muhittin Mungan

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38 Scopus citations

Abstract

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 ≤ 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.

Original language	English (US)
Pages (from-to)	409-420
Number of pages	12
Journal	Physica D: Nonlinear Phenomena
Volume	83
Issue number	4
DOIs	https://doi.org/10.1016/0167-2789(95)00042-3
State	Published - Jun 1 1995
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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10.1016/0167-2789(95)00042-3

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abstract = "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 rc. For r >rc, the system can be understood in terms of a conventional billiard in an infinite wedge. For r ≤ rc, 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.",

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AU - Grossman, Elizabeth

AU - Mungan, Muhittin

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N2 - 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 rc. For r >rc, the system can be understood in terms of a conventional billiard in an infinite wedge. For r ≤ rc, 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.

AB - 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 rc. For r >rc, the system can be understood in terms of a conventional billiard in an infinite wedge. For r ≤ rc, 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.

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Inelastic collisions of three particles on a line as a two-dimensional billiard

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