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arXiv · 1607.00580

The Broucke-H\'enon orbit and the Schubart Orbit in the planar three-body problem with equal masses

Wentian Kuang·Tiancheng Ouyang·Zhifu Xie·Duokui Yan
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Abstract

In this paper, we study the variational properties of two special orbits: the Schubart orbit and the Broucke-H\'{e}non orbit. We show that under an appropriate topological constraint, the action minimizer must be either the Schubart orbit or the Broucke-H\'{e}non orbit. One of the main challenges is to prove that the Schubart orbit coincides with the action minimizer connecting a collinear configuration with a binary collision and an isosceles configuration. A new geometric argument is introduced to overcome this challenge.

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Wentian Kuang, Tiancheng Ouyang, Zhifu Xie, Duokui Yan. 2016-07-03. The Broucke-H\'enon orbit and the Schubart Orbit in the planar three-body problem with equal masses. https://arxiv.org/abs/1607.00580

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