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New stacked central configurations for the planar 5-body problem

  • Jaume LlibreEmail author
  • Luis Fernando Mello
  • Ernesto Perez-Chavela
Original Article

Abstract

A stacked central configuration in the n-body problem is one that has a proper subset of the n-bodies forming a central configuration. In this paper we study the case where three bodies with masses m 1, m 2, m 3 (bodies 1, 2, 3) form an equilateral central configuration, and the other two with masses m 4, m 5 are symmetric with respect to the mediatrix of the segment joining 1 and 2, and they are above the triangle generated by {1, 2, 3}. We show the existence and non-existence of this kind of stacked central configurations for the planar 5-body problem.

Keywords

Planar central configurations n-body problem Stacked central configurations 5-body problem 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Jaume Llibre
    • 1
    Email author
  • Luis Fernando Mello
    • 2
  • Ernesto Perez-Chavela
    • 3
  1. 1.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBellaterra, Barcelona, CataloniaSpain
  2. 2.Instituto de Ciências ExatasUniversidade Federal de ItajubáItajubáBrazil
  3. 3.Departamento de MatemáticasUAM-IztapalapaIztapalapa, MexicoMexico

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