Numerical Exploration of the Limit Ring Problem

• E. Barrabés ^[1] ; J. M. Cors ^[2] ; G. R. Hall ^[3]
  1. [1] Universitat de Girona

     Universitat de Girona

     Gerona, España

     
  2. [2] Universitat Politècnica de Catalunya

     Universitat Politècnica de Catalunya

     Barcelona, España

     
  3. [3] Boston University

     Boston University

     City of Boston, Estados Unidos

     

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 12, Nº 1, 2013, págs. 25-52
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • The aim of this work is to provide an insight of an idealized model of a planetary ring. The model is a limit case of the planar circular restricted 1 + n body problem, where an infinitesimal particle moves under the gravitational influence of a large central body and n smaller bodies located on the vertices of a regular n-gon.When considering n tending to infinity, a model depending on one parameter is obtained.

    We study the main important structures of the problem depending on this parameter (equilibria, Hill’s regions, linear stability, …). We use Poincaré maps, for different values of the parameter, in order to predict the width of the ring and the richness of the dynamics that occur is discussed. This work is a continuation of the work presented in Barrabés by (SIAM J Appl Dyn Syst 9:634–658, 2010).