English

From Brake to Syzygy

Dynamical Systems 2015-05-30 v1

Abstract

In the planar three-body problem, we study solutions with zero initial velocity (brake orbits). Following such a solution until the three masses become collinear (syzygy), we obtain a continuous, flow-induced Poincar\'e map. We study the image of the map in the set of collinear configurations and define a continuous extension to the Lagrange triple collision orbit. In addition we provide a variational characterization of some of the resulting brake-to-syzygy orbits and find simple examples of periodic brake orbits.

Keywords

Cite

@article{arxiv.1109.1089,
  title  = {From Brake to Syzygy},
  author = {Richard Moeckel and Richard Montgomery and Andrea Venturelli},
  journal= {arXiv preprint arXiv:1109.1089},
  year   = {2015}
}
R2 v1 2026-06-21T19:00:17.406Z