From Brake to Syzygy

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 Poincaré 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.

References in corpus (2)

• Action minimizing solutions of the Newtonian n-body problem: from homology to symmetry
• A trial symbolic dynamics of the planar three-body problem

Cited by in corpus (8)

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• Free time minimizers for the planar three-body problem
• Shape Space Figure-$8$ Solution of Three Body Problem with Two Equal Masses
• Symmetric Regularization, Reduction and Blow-Up of the Planar Three-Body Problem
• Symbolic dynamics for the anisotropic $N$-centre problem at negative energies
• Symmetric Periodic Orbits in Three Sub-Problems of the N-body Problem
• Geometric properties of minimizers in the planar three-body problem with two equal masses