Central configurations in the five-body problem : Rhombus plus one
Cornelio, J. Lino (Universidad Juárez Autónoma de Tabasco (Mèxic). División Académica de Ciencias Básicas)
Álvarez-Ramírez, Martha (Universidad Autónoma Metropolitana-Iztapalapa (Mèxic))
Cors Iglesias, Josep Maria (Universitat Politècnica de Catalunya. Departament de Matemàtiques)

Date:	2021
Abstract:	We show the existence of central configurations in the planar five-body problem where four bodies are located at the vertices of a rhombus, called rhombus plus one central configurations. Concretely we prove analytically their existence when one diagonal is nearly equal to the sides of the rhombus and when the two diagonals are either equal or nearly equal. In addition, we prove that given a rhombus plus one configuration, the corresponding vector of positive masses that makes the configuration central, if exists, is unique.
Grants:	Agencia Estatal de Investigación PID2019-104658GB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Five-body problem ; Central configuration ; Rhombus configuration ; Square configuration
Published in:	Qualitative theory of dynamical systems, Vol. 20, Issue 2 (July 2021) , art. 51, ISSN 1662-3592

DOI: 10.1007/s12346-021-00486-6

Postprint 14 p, 396.8 KB

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