  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 no-slip has been used. In recent work, it has become
apparent that no-slip billiards resemble non-holonomic 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 non-holonomic (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.
