The Integrability of a knife-edge Billiard in a Disk
Alejandro Bravo-Doddoli, Huaidian Hou, William Clark, Anthony M. Bloch
Abstract
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.
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