Convexity and symmetry of central configurations in the five-body problem: Lagrange plus two

• Barrabés, E. ^[1] ; Cors, J. M. ^[2] ; Fernandes, A. C. ^[3] ; Vidal, C. ^[4]
  1. [1] Universitat de Girona

     Universitat de Girona

     Gerona, España

     
  2. [2] Universitat Politècnica de Catalunya

     Universitat Politècnica de Catalunya

     Barcelona, España

     
  3. [3] Universidade Federal de Itajubá

     Universidade Federal de Itajubá

     Brasil

     
  4. [4] Universidad del Bío-Bío

     Universidad del Bío-Bío

     Comuna de Concepción, Chile

     

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 20, Nº 3, 2021
• Idioma: inglés
• DOI: 10.1007/s12346-021-00504-7
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• Resumen

  • We study convexity and symmetry of central configurations in the five body problem when three of the masses ara located at the vertices of an equilateral triangle, that we call Lagrange plus two central configurations. First, we prove that the two bodies out of the vertices of the triangle cannot be placed on certain lines. Next, we give a geometrical characterization of such configurations in the sense as that of Dziobek, and we describe the admissible regions where the two remaining bodies can be placed. Furthermore, we prove that any Lagrange plus two central configuration is concave. Finally, we show numerically the existence of non-symmetric central configurations of the five body problem.

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