Double-Antiprism Central Configurations of the 3n-Body Problem

Montserrat Corbera ^[1] ; Jaume Llibre
1. [1] Universitat de Vic
  
  Universitat de Vic
  
  Vich, España
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 12, Nº 1, 2013, págs. 11-24
Idioma: inglés
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Resumen
- In this paper we study numerically a new type of central configurations of the 3n-body problem with equal masses which consist of three n-gons contained in three planes z = 0 and z = ±β = 0. The n-gon on z = 0 is scaled by a factor α and it is rotated by an angle of π/n with respect to the ones on z = ±β. In this kind of configurations, the masses on the planes z = 0 and z = β are at the vertices of an antiprism with bases of different size. The same occurs with the masses on z = 0 and z = −β. We call this kind of central configurations double-antiprism central configurations. We will show the existence of central configurations of this type.