Trapezoid central configurations

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...

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Vydáno v:	Applied mathematics and computation Ročník 346; s. 127 - 142
Hlavní autoři:	Corbera, Montserrat, Cors, Josep M., Llibre, Jaume, Pérez-Chavela, Ernesto
Médium:	Journal Article Publikace
Jazyk:	angličtina
Vydáno:	Elsevier Inc 01.04.2019
Témata:	37 Dynamical systems and ergodic theory 37N Applications 4-body problem 70 Mechanics of particles and systems 70F Dynamics of a system of particles, including celestial mechanics Classificació AMS Configurations Convex central configurations Enginyeria mecànica Many-body problem Matemàtiques i estadística Problema dels cossos múltiples Trapezoidal central configurartions Àrees temàtiques de la UPC 4-body problem 70F10 Convex central configurations 70F15 37N05 Trapezoidal central configurartions
ISSN:	0096-3003, 1873-5649
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Popis
Shrnutí:	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.
ISSN:	0096-3003 1873-5649
DOI:	10.1016/j.amc.2018.10.066