Qualitative Theory of Dynamical Systems

, Volume 12, Issue 1, pp 25–52 | Cite as

Numerical Exploration of the Limit Ring Problem

  • E. Barrabés
  • J. M. CorsEmail author
  • G. R. Hall


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).


Celestial Mechanics N body problem Planetary rings 

Mathematics Subject Classification (2000)

70F15 70F45 70K42 70K43 37N05 


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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Departament d’Informàtica i Matemàtica AplicadaUniversitat de GironaGironaSpain
  2. 2.Departament de Matemàtica Aplicada IIIUniversitat Politècnica de CatalunyaBarcelonaSpain
  3. 3.Department of Mathematics and StatisticsBoston UniversityBostonUSA

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