论文标题
滚动系统及其台球限制
Rolling systems and their billiard limits
论文作者
论文摘要
从广义上讲，台球系统可以被视为机械系统的模型，其中刚性部分通过弹性冲动（碰撞）力相互作用。当需要或必要考虑涉及球形体的碰撞中的线性/角动量交换时，通常使用了一种台球系统。在最近的工作中，很明显，无滑动台球以多种方式类似于非全面的机械系统。基于Borisov，Kilin和Mamaev的一个想法，我们表明，不滑动台球通常是非全面（滚动）系统的限制，其方式类似于普通台球作为如何通过Riemannian歧管的扁平化而作为地球流动的限制出现的。
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.
