From Brake to Syzygy

Details From Brake to Syzygy From Brake to Syzygy

2011-09-06

arxiv.org/abs/1109.1089v1

Mathematics

Dynamical Systems

Scientific paper

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.

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