Central configurations of the 4-body problem with masses m_1=m_2&gt;m_3=m_4=m&gt;0 and m small

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(Universitat de Vic. Departament de Tecnologies Digitals i de la Informació)
Llibre, Jaume

(Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Fecha:	2014
Resumen:	In this paper we give a complete description of the families of central configurations of the planar 4-body problem with two pairs of equals masses and two equal masses sufficiently small. In particular, we give an analytical proof that this particular 4-body problem has exactly 34 different classes of central configurations. Moreover for this problem we prove the following two conjectures: There is a unique convex planar central configuration of the 4-body problem for each ordering of the masses in the boundary of its convex hull, which appears in [3]. We also prove the conjecture: There is a unique convex planar central configuration having two pairs of equal masses located at the adjacent vertices of the configuration and it is an isosceles trapezoid. Finally, the families of central configurations of this 4-body problem are numerically continued to the 4-body problem with four equal masses.
Ayudas:	Ministerio de Ciencia e Innovación MTM 2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 European Commission 316338 European Commission 318999
Derechos:	Tots els drets reservats.
Lengua:	Anglès
Documento:	Article ; recerca ; Versió acceptada per publicar
Materia:	4-body problem ; Central configurations ; Two-small masses ; Convex central configurations ; Trapezoidal central configurations
Publicado en:	Applied Mathematics and Computation, Vol. 246 (2014) , p. 121-147, ISSN 1873-5649

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