Home > Articles > Published articles > Trapezoid central configurations |
Date: | 2019 |
Abstract: | We classify all planar four-body central configurations where two pairs of the bodies are on parallel lines. Using cartesian coordinates, we show that the set of four-body trapezoid central configurations with positive masses forms a two-dimensional surface where two symmetric families, the rhombus and isosceles trapezoid, are on its boundary. We also prove that, for a given position of the bodies, in some cases a specific order of the masses determines the geometry of the configuration, namely acute or obtuse trapezoid central configuration. We also prove the existence of non-symmetric trapezoid central configurations with two pairs of equal masses. |
Grants: | Ministerio de Economía y Competitividad MTM2016-77278-P European Commission 777911 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 |
Rights: | Tots els drets reservats. |
Language: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Subject: | 4-body problem ; Convex central configurations ; Trapezoidal central configurartions |
Published in: | Applied Mathematics and Computation, Vol. 346 (April 2019) , p. 127-142, ISSN 0096-3003 |
Postprint 31 p, 10.1 MB |