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 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.

广义上讲，台球系统可以看作是机械系统的模型，其中刚性零件通过弹性脉冲（碰撞）力相互作用。当需要或有必要在涉及球形物体的碰撞中考虑线性/角动量交换时，通常使用一种称为无滑的台球系统。在最近的工作中，很明显，防滑台球在许多方面类似于非完整的机械系统。根据鲍里索夫（Borisov），基林（Kilin）和马马耶夫（Mamaev）的观点，我们表明，无滑台球通常作为非完整（滚动）系统的极限而产生，其方式类似于普通台球如何随着测地线的展平而随着测地流量的极限而产生。黎曼流形