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JOURNALS // Regular and Chaotic Dynamics // Archive

Regul. Chaotic Dyn., 2021 Volume 26, Issue 1, Pages 1–21 (Mi rcd1099)

This article is cited 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.

MSC: 70F25

Received: 19.09.2020
Accepted: 21.12.2020

Language: English

DOI: 10.1134/S1560354721010019



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