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arXiv · 2504.17645

A common first integral from three-body secular theory and Kepler billiards

Gabriella Pinzari·Lei Zhao
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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.

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Gabriella Pinzari, Lei Zhao. 2025-04-24. A common first integral from three-body secular theory and Kepler billiards. https://arxiv.org/abs/2504.17645

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