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Avoiding collisions under topological constraints in variational problems coming from celestial mechanics

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Abstract

In a singular potential setting, we generalize a method which allows to show that minimizers under topological constraints of the action functional (or of the Maupertuis one) are collision-free. This methods applies to 3-dimensional problems of celestial mechanics exhibiting a particular cylindrical symmetry, as well as to planar problems of N-centre type, where it gives optimal results.

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Authors and Affiliations

  1. Mathematisches Institut, Justus-Liebig-Universität Gießen, Arndtstraße 2, 35392, Gießen, Germany

    Nicola Soave

  2. Dipartimento di Matematica “Giuseppe Peano”, Università di Torino, Via Carlo Alberto 10, 10123, Torino, Italy

    Susanna Terracini

Authors
  1. Nicola Soave
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  2. Susanna Terracini
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Correspondence to Susanna Terracini.

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To Yvonne Choquet-Bruhat with great admiration

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Soave, N., Terracini, S. Avoiding collisions under topological constraints in variational problems coming from celestial mechanics. J. Fixed Point Theory Appl. 14, 457–501 (2013). https://doi.org/10.1007/s11784-014-0174-3

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  • DOI: https://doi.org/10.1007/s11784-014-0174-3

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