Convexity and symmetry of central configurations in the five-body problem: Lagrange plus two

We study convexity and symmetry of central configurations in the five body problem when three of the masses ara located at the vertices of an equilateral triangle, that we call Lagrange plus two central configurations. First, we prove that the two bodies out of the vertices of the triangle cannot be...

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Detalles Bibliográficos
Autores: Barrabés Vera, Esther, Cors Iglesias, Josep Maria, Fernandes, A.C., Vidal, Claudio
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2021
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:10256/19707
Acceso en línea:http://hdl.handle.net/10256/19707
Access Level:acceso abierto
Palabra clave:Mecànica celest
Celestial mechanics
Lagrange, Espais de
Lagrange spaces
Geometria diferencial
Geometry, Differencial
Problema dels cossos múltiples
Many-body problem
Descripción
Sumario:We study convexity and symmetry of central configurations in the five body problem when three of the masses ara located at the vertices of an equilateral triangle, that we call Lagrange plus two central configurations. First, we prove that the two bodies out of the vertices of the triangle cannot be placed on certain lines. Next, we give a geometrical characterization of such configurations in the sense as that of Dziobek, and we describe the admissible regions where the two remaining bodies can be placed. Furthermore, we prove that any Lagrange plus two central configuration is concave. Finally, we show numerically the existence of non-symmetric central configurations of the five body problem