The Broucke-Hénon Orbit and the Schubart Orbit In the Planar Three-Body Problem With Two Equal Masses
Document Type
Article
Publication Date
10-21-2019
Department
Mathematics
School
Mathematics and Natural Sciences
Abstract
© 2019 IOP Publishing Ltd & London Mathematical Society. In this paper, we study the variational properties of two special orbits: a Schubart orbit and a Broucke-Hénon orbit. We show that under an appropriate topological constraint, a minimizer must be either a Schubart orbit or a Broucke-Hénon orbit. One of the main challenges is to prove that a Schubart orbit coincides with a minimizer connecting a collinear configuration with a binary collision and an isosceles configuration. A new geometric argument is introduced to overcome this challenge.
Publication Title
Nonlinearity
Volume
32
Issue
12
First Page
4639
Last Page
4664
Recommended Citation
Kuang, W.,
Ouyang, T.,
Xie, Z.,
Yan, D.
(2019). The Broucke-Hénon Orbit and the Schubart Orbit In the Planar Three-Body Problem With Two Equal Masses. Nonlinearity, 32(12), 4639-4664.
Available at: https://aquila.usm.edu/fac_pubs/17976