From Brake to Syzygy

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 defi...

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Bibliographic Details
Published in:Archive for rational mechanics and analysis 2012-06, Vol.204 (3), p.1009-1060
Main Authors: Moeckel, Richard, Montgomery, Richard, Venturelli, Andrea
Format: Article
Language:English
Subjects:
Classical Mechanics
Complex Systems
Dynamical Systems
Fluid- and Aerodynamics
Mathematical and Computational Physics
Mathematics
Physics
Physics and Astronomy
Theoretical
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Summary: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.
ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-012-0502-y