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

Double-Antiprism Central Configurations of the 3n-Body Problem
 
Corbera Subirana, Montserrat ; Llibre, Jaume
2013

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Enllaç permanent: http://hdl.handle.net/10854/2201
 
Versió de l'editor: https://doi.org/10.1007/s12346-012-0076-y
 

Abstract

Abstract 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 ...»»»»
Abstract 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.^^^^

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Citation:

Corbera, Montserrat, Jaume LLibre. "Double-Antiprism Central Configurations of the 3n-Body Problem" A: Qualitative Theory of Dynamical Systems, April 2013, Volume 12, Issue 1, pp. 11-24