论文标题
粗暴的碰撞
Rough Collisions
论文作者
论文摘要
粗糙的碰撞定律描述了一对粗糙的刚体的限制接触动力学，因为每个身体表面的粗糙特征（s骨）的比例为零。粗糙碰撞法的类别非常大，包括随机元素。我们的主要结果是在维度2中自由移动的粗糙磁盘和固定的粗糙墙的粗糙碰撞定律表征。（i）在台球理论的某些众所周知的众所周知的不变措施中对称的任何碰撞定律，以及（ii）保守相位空间速度的投影到“滚动速度”上。我们还提供了一种方法，可以明确构建粗糙的碰撞定律，以在磁盘和墙壁上多种微观结构选择。在我们的介绍中，我们审查了过去在台球的工作，包括其他粗糙台球系统的特征，我们的结果基于这一点。
A rough collision law describes the limiting contact dynamics of a pair of rough rigid bodies, as the scale of the rough features (asperities) on the surface of each body goes to zero. The class of rough collision laws is quite large and includes random elements. Our main results characterize the rough collision laws for a freely moving rough disk and a fixed rough wall in dimension 2. Any collision law which (i) is symmetric with respect to a certain well-known invariant measure from billiards theory, and (ii) conserves the projection of the phase space velocity onto the "rolling velocity" is a rough collision law. We also provide a method for explicitly constructing rough collision laws for a broad range of choices of microstructure on the disk and wall. In our introduction, we review past work in billiards, including characterizations of other rough billiard systems, which our results build upon.
