Title

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

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