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arXiv · 2301.00193

The Schubart orbits on the circle

Shuqiang Zhu
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Abstract

We consider the three body problem on $S^1$ under the cotangent potential. We first construct homothetic orbits ending in singularities, including total collision singularity and collision-antipodal singularity. Then certain symmetrical periodic orbits with two equal masses, called Schubart orbits, are shown to exist. The proof is based on the construction of a Wazewski set in the phase space.

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Shuqiang Zhu. 2022-12-31. The Schubart orbits on the circle. https://arxiv.org/abs/2301.00193

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