A class of spatial central configurations in Newtonian 8-body problems

• Liang Ding ^[1] ; Zaili Yang ^[1] ; Pengfei Yuan ^[2]
  1. [1] Guizhou Minzu University

     Guizhou Minzu University

     China

     
  2. [2] Southwest University

     Southwest University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 5, 2025
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • For Newtonian 8-body problems, we investigate a class of spatial configurations consisting of two parallel rhombuses separated by a distance h > 0. In these configurations, four masses m1, m2, m3, and m4 are positioned counterclockwise at the vertices of one rhombus, while the other four masses m 1, m 2, m 3, and m 4 are positioned counterclockwise at the vertices of the second rhombus.We obtain the necessary conditions and sufficient conditions for the existence of these spatial central configurations. Specifically, in the central configurations, we find that if either m j = m j for all j ∈ {1, 2, 3, 4}, or the two rhombuses have equal sizes, then both rhombuses must necessarily be squares.

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