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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Bibliographic Details
Published in:Applied mathematics and computation Vol. 346; pp. 127 - 142
Main Authors: Corbera, Montserrat, Cors, Josep M., Llibre, Jaume, Pérez-Chavela, Ernesto
Format: Journal Article Publication
Language:English
Published: Elsevier Inc 01.04.2019
Subjects:
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
Online Access:Get full text
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Summary: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