The Broucke-Hénon Orbit and the Schubart Orbit In the Planar Three-Body Problem With Two Equal Masses
Mathematics and Natural Sciences
© 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.
(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