The Broucke-Hénon orbit and the Schubart Orbit in the planar three-body problem with equal masses

Abstract

In this paper, we study the variational properties of two special orbits: the Schubart orbit and the Broucke-Hénon orbit. We show that under an appropriate topological constraint, the action minimizer must be either the Schubart orbit or the Broucke-Hénon 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.

32 pages, 4 figures

References in corpus (2)

• A new variational method with SPBC and many stable choreographic solutions of the Newtonian 4-body problem
• Existence of prograde double-double orbits in the equal-mass four-body problem

Cited by in corpus (2)

• Existence of prograde double-double orbits in the equal-mass four-body problem
• Action minimizers under topological constraints in the planar equal-mass four-body problem