A common first integral from three-body secular theory and Kepler billiards
Dynamical Systems
2025-11-27 v2
Abstract
We observe that a particular first integral of the partially-averaged system in the secular theory of the three-body problem appears also as an important conserved quantity of integrable Kepler billiards. In this note we illustrate their common roots with the projective dynamics of the two-center problem. We then combine these two aspects to define a class of integrable billiard systems on surfaces of constant curvature.
Keywords
Cite
@article{arxiv.2504.17645,
title = {A common first integral from three-body secular theory and Kepler billiards},
author = {Gabriella Pinzari and Lei Zhao},
journal= {arXiv preprint arXiv:2504.17645},
year = {2025}
}
Comments
correct some mistakes and update references. 11 pages