On central configurations of the kn-body problem

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

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Detalles Bibliográficos
Autores: Barrabés Vera, Esther, Cors Iglesias, Josep Maria|||0000-0002-9803-8490
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/132982
Acceso en línea:https://hdl.handle.net/2117/132982
https://dx.doi.org/10.1016/j.jmaa.2019.04.010
Access Level:acceso abierto
Palabra clave:Celestial mechanics
Many-body problem
N-body problem
Planar central configurations
Twisted central configurations
Mecànica celest
Problema dels cossos múltiples
Classificació AMS::70 Mechanics of particles and systems::70F Dynamics of a system of particles, including celestial mechanics
Àrees temàtiques de la UPC::Matemàtiques i estadística
Descripción
Sumario:We consider planar central configurations of the Newtonian kn-body problem consisting in k groups of regular n-gons of equal masses, called (k, n)-crown. We derive the equations of central configurations for a general (k, n)-crown. When k = 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.