On central configurations of the κn-body problem

We consider planar central configurations of the Newtonian κn-body problem consisting in κ groups of regular n-gons of equal masses, called (κ,n)-crown. We derive the equations of central configurations for a general (κ,n)-crown. When κ=2 we prove the existence of a twisted (2,n)-crown for any value...

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Bibliographic Details
Authors: Barrabés Vera, Esther|||0000-0002-8448-692X, Cors Iglesias, Josep Maria|||0000-0002-9803-8490
Format: article
Publication Date:2019
Country:España
Institution:Universitat Autònoma de Barcelona
Repository:Dipòsit Digital de Documents de la UAB
Language:English
OAI Identifier:oai:ddd.uab.cat:204399
Online Access:https://ddd.uab.cat/record/204399
https://dx.doi.org/urn:doi:10.1016/j.jmaa.2019.04.010
Access Level:Open access
Keyword:Celestial mechanics
N-body problem
Planar central configurations
Twisted central configurations
Description
Summary:We consider planar central configurations of the Newtonian κn-body problem consisting in κ groups of regular n-gons of equal masses, called (κ,n)-crown. We derive the equations of central configurations for a general (κ,n)-crown. When κ=2 we prove the existence of a twisted (2,n)-crown for any value of the mass ratio. Moreover, for n=3,4 and any value of the mass ratio, we give the exact number of twisted (2,n)-crowns, and describe their location. Finally, we conjecture that for any value of the mass ratio there exist exactly three (2,n)-crowns for n≥5.