Central Configurations in the Five-Body Problem: Rhombus Plus One

• Lino Cornelio, J. ^[1] ; Alvarez-Ramírez, Martha ^[3] ; Cors, Josep M. ^[2]
  1. [1] Universidad Juárez Autónoma de Tabasco

     Universidad Juárez Autónoma de Tabasco

     México

     
  2. [2] Universitat Politècnica de Catalunya

     Universitat Politècnica de Catalunya

     Barcelona, España

     
  3. [3] UAM-Iztapalapa

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 20, Nº 2, 2021
• Idioma: inglés
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• Resumen

  • We show the existence of central configurations in the planar five-body problem where four bodies are located at the vertices of a rhombus, called rhombus plus one central configurations. Concretely we prove analytically their existence when one diagonal is nearly equal to the sides of the rhombus and when the two diagonals are either equal or nearly equal. In addition, we prove that given a rhombus plus one configuration, the corresponding vector of positive masses that makes the configuration central, if exists, is unique.