The Broucke-H\'enon orbit and the Schubart Orbit in the planar three-body problem with equal masses
Dynamical Systems
2017-10-30 v2
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.
Keywords
Cite
@article{arxiv.1607.00580,
title = {The Broucke-H\'enon orbit and the Schubart Orbit in the planar three-body problem with equal masses},
author = {Wentian Kuang and Tiancheng Ouyang and Zhifu Xie and Duokui Yan},
journal= {arXiv preprint arXiv:1607.00580},
year = {2017}
}
Comments
32 pages, 4 figures