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This article is cited in 1 scientific paper (total in 1 paper)
Rolling Systems and Their Billiard Limits
Christopher Coxa, Renato Feresb, Bowei Zhaob a Department of Mathematics, University of Delaware,
Ewing Hall, DE 19711 Newark, USA
b Department of Mathematics and Statistics, Washington University,
Campus Box 1146, MO 63130 St. Louis, USA
Abstract:
Billiard systems, broadly speaking, may be regarded as models of mechanical
systems in which rigid parts interact through elastic impulsive (collision) forces. When it is
desired or necessary to account for linear/angular momentum exchange in collisions involving
a spherical body, a type of billiard system often referred to as <i>no-slip</i> has been used. In recent
work, it has become apparent that no-slip billiards resemble nonholonomic mechanical systems
in a number of ways. Based on an idea by Borisov, Kilin and Mamaev, we show that no-slip
billiards very generally arise as limits of nonholonomic (rolling) systems, in a way that is akin to
how ordinary billiards arise as limits of geodesic flows through a flattening of the Riemannian
manifold.
Keywords:
no-slip billiards, nonholonomic systems.
Received: 19.09.2020 Accepted: 21.12.2020
Citation:
Christopher Cox, Renato Feres, Bowei Zhao, “Rolling Systems and Their Billiard Limits”, Regul. Chaotic Dyn., 26:1 (2021), 1–21
Linking options:
https://www.mathnet.ru/eng/rcd1099 https://www.mathnet.ru/eng/rcd/v26/i1/p1
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Abstract page: | 81 | References: | 16 |
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