Linear Stability of the n-gon Relative Equilibria of the (1 + n)-Body Problem

• Xingbo Xu ^[1]
  1. [1] Chinese Academy of Sciences

     Chinese Academy of Sciences

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 12, Nº 1, 2013, págs. 255-271
• Idioma: inglés
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• Resumen

  • We consider the linear stability of the regular n-gon relative equilibria of the (1+n)-body problem. It is shown that there exist at most two kinds of infinitesimal bodies arranged alternatively at the vertices of a regular n-gon when n is even, and only one set of identical infinitesimal bodies when n is odd. In the case of n even, the regular n-gon relative equilibrium is shown to be linearly stable when n 14. In each case of n = 8, 10 and 12, linear stability can also be preserved if the ratio of two kinds of masses belongs to an open interval. When n is odd, the related conclusion on the linear stability is recalled.