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arXiv · 2609.12963

The Integrability of a knife-edge Billiard in a Disk

Alejandro Bravo-Doddoli·Huaidian Hou·William Clark·Anthony M. Bloch
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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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Alejandro Bravo-Doddoli, Huaidian Hou, William Clark, Anthony M. Bloch. 2026-09-11. The Integrability of a knife-edge Billiard in a Disk. https://arxiv.org/abs/2609.12963

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