圆盘中刀口台球的可积性
The Integrability of a knife-edge Billiard in a Disk
- University of Michigan（密歇根大学）
- Ohio University（俄亥俄大学）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文证明了圆盘中刀口非完整台球的可积性，通过参数化碰撞空间并构造递推映射，并揭示了其广义焦散线族。
中文摘要 AI 辅助
本文证明了由圆盘中刀口定义的非完整台球的可积性。文章首先利用揭示系统旋转对称性的坐标对碰撞空间进行参数化，然后在碰撞后状态空间上构造一个映射，通过递推关系将每个碰撞后状态与下一个状态联系起来，从而编码台球动力学。此外，文章还表明刀口台球具有一族广义焦散线。
英文摘要
This paper proves the integrability of a nonholonomic billiard defined by a knife-edge in a disk. The paper begins by parametrizing the impact space using coordinates that reveal the system's rotational symmetry. It then constructs a map on the space of post-impact states that encodes the billiard dynamics through a recurrence relating each post-impact state to the next. In addition, the paper shows that the knife-edge billiard admits a family of generalized caustics.
