English

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