Work

The Integrability of a knife-edge Billiard in a Disk

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.12963

Authors: Bravo-Doddoli, Alejandro, Hou, Huaidian, Clark, William, Bloch, Anthony M.

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, University of Michigan, Multidisciplinary University Research Initiative, Air Force Office of Scientific Research

Awards: Dynamics, Integrability, and Control of Mechanical and Physical Systems, Dynamics, Integrability and Control of Mechanical and Physical Systems, G946381479

OpenAlex ID: W7212628456

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