On Stacked Planar Central Configurations with Five Bodies when One Body is Removed

• Antonio Carlos Fernandes ^[1] ; Luis Fernando Mello ^[1]
  1. [1] Universidade Federal de Itajubá

     Universidade Federal de Itajubá

     Brasil

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 12, Nº 2, 2013, págs. 293-303
• Idioma: inglés
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• Resumen

  • In this paper we answer the following question posed by Hampton (Nonlinearity 18:2299–2304, 2005). In addition to symmetric collinear configurations and the square with a mass at its center are there any planar five-body central configurations with a subset forming a four-body central configuration? We prove that, for non-collinear configurations, the only possible strictly planar central configuration for the five-body problem for which it can be removed one body such that the remaining four bodies are already in a central configuration is obtained with four bodies of equal masses at the vertices of a square and the fifth body of arbitrary mass at the center of the square.