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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 |
Postprint 14 p, 396.8 KB |