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: | , , , |
|---|---|
| Formato: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:204380 |
| Acesso em linha: | https://ddd.uab.cat/record/204380 https://dx.doi.org/urn:doi:10.1016/j.amc.2018.10.066 |
| Access Level: | acceso abierto |
| Palavra-chave: | 4-body problem Convex central configurations Trapezoidal central configurartions |
| Resumo: | 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. |
|---|