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PreprintarXiv licencearXiv

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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Cite

BibTeXRIS
BibTeX
@misc{bravododdoli2026integrability,
  title = {{The Integrability of a knife-edge Billiard in a Disk}},
  author = {Alejandro Bravo-Doddoli and Huaidian Hou and William Clark and Anthony M. Bloch},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.12963},
  eprint = {2609.12963},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12963},
}
RIS
TY  - UNPB
TI  - The Integrability of a knife-edge Billiard in a Disk
AU  - Alejandro Bravo-Doddoli
AU  - Huaidian Hou
AU  - William Clark
AU  - Anthony M. Bloch
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.12963
UR  - https://arxiv.org/abs/2609.12963
AB  - 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.
ER  -