Rolling Systems and Their Billiard Limits

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 collisions involving a spherical body, type billiard system often referred no-slip has been used. In recent work, become apparent that billiards resemble non-holonomic number ways. Based on an idea by Borisov, Kilin and Mamaev, we show very generally arise limits (rolling) way akin how ordinary geodesic flows flattening the Riemannian manifold.