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...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/125162 |
| Acceso en línea: | https://hdl.handle.net/2117/125162 https://dx.doi.org/10.1016/j.amc.2018.10.066 |
| Access Level: | acceso abierto |
| Palabra clave: | Many-body problem Configurations 4-body problem Convex central configurations Trapezoidal central configurartions Problema dels cossos múltiples Classificació AMS::70 Mechanics of particles and systems::70F Dynamics of a system of particles, including celestial mechanics Classificació AMS::37 Dynamical systems and ergodic theory::37N Applications Àrees temàtiques de la UPC::Matemàtiques i estadística Àrees temàtiques de la UPC::Enginyeria mecànica |
| Sumario: | 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. |
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