Convex central configurations of the 4-body problem with two pairs of equal masses
Fernandes, Antonio Carlos (Universidade Federal de Itajubá (Brasil). Instituto de Matemática e Computação)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Mello, Luis Fernando (Universidade Federal de Itajubá (Brasil). Instituto de Matemática e Computação)

Date:	2017
Abstract:	MacMillan and Bartky in 1932 proved that there is a unique isosceles trapezoid central configuration of the 4--body problem when two pairs of equal masses are located at adjacent vertices. After this result the following conjecture was well known between people working on central configurations: The isosceles trapezoid is the unique convex central configuration of the planar 4--body problem when two pairs of equal masses are located at adjacent vertices. We prove this conjecture.
Grants:	Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 316338 European Commission 318999 Ministerio de Economía y Competitividad MTM2013-40998-P
Note:	Agraïments: The first and third authors are partially supported by FAPEMIG grant APQ-001082/14. The third author is partially supported by CNPq grant 472321/2013-7 and by FAPEMIG grant PPM-00516-15. The second and third autors are supported by CAPES CSF-PVE grant 88881.030454/2013-01.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	4-body problem ; Celestial mechanics ; Convex central configuration ; Planar central configuration
Published in:	Archive for Rational Mechanics and Analysis, 2017 , ISSN 1432-0673

DOI: 10.1007/s00205-017-1134-z

Postprint 17 p, 410.5 KB

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