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From Brake to Syzygy

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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.

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Authors and Affiliations

  1. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Richard Moeckel

  2. Department of Mathematics, University of California, Santa Cruz, CA, USA

    Richard Montgomery

  3. Laboratoire d’Analyse non linéaire et géométrie, Université d’Avignon, Avignon, France

    Andrea Venturelli

Authors
  1. Richard Moeckel
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  2. Richard Montgomery
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  3. Andrea Venturelli
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Correspondence to Andrea Venturelli.

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Communicated by P. Rabinowitz

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Moeckel, R., Montgomery, R. & Venturelli, A. From Brake to Syzygy. Arch Rational Mech Anal 204, 1009–1060 (2012). https://doi.org/10.1007/s00205-012-0502-y

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  • DOI: https://doi.org/10.1007/s00205-012-0502-y

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