On the existence of bi-pyramidal central configurations of the n 2-body problem with an n-gon base

In this paper we prove the existence of central configurations of the n + 2-body problem where n equal masses are located at the vertices of a regular n-gon and the remaining 2 masses, which are not necessarily equal, are located on the straight line orthogonal to the plane containing the n-gon pass...

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Detalles Bibliográficos
Autores: Corbera Subirana, Montserrat|||0000-0002-0367-9667, Llibre, Jaume|||0000-0002-9511-5999
Tipo de recurso: artículo
Fecha de publicación:2013
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:150631
Acceso en línea:https://ddd.uab.cat/record/150631
https://dx.doi.org/urn:doi:10.3934/dcds.2013.33.1049
Access Level:acceso abierto
Palabra clave:Spatial central configurations
N + 2-body problem
Bi-pyramidal central configurations
Descripción
Sumario:In this paper we prove the existence of central configurations of the n + 2-body problem where n equal masses are located at the vertices of a regular n-gon and the remaining 2 masses, which are not necessarily equal, are located on the straight line orthogonal to the plane containing the n-gon passing through its center. Here this kind of central configurations is called bi-pyramidal central configurations. In particular, we prove that if the masses mn+1 and mn+2 and their positions satisfy convenient relations, then the configuration is central. We give explicitly those relations.