Central configurations in the five-body problem: rhombus plus one
We show the existence of central configurations in the planar five-body problem where four bodies are located at the vertices of a rhombus, called rhombus plus one central configurations. Concretely we prove analytically their existence when one diagonal is nearly equal to the sides of the rhombus a...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| 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:2117/352053 |
| Acceso en línea: | https://hdl.handle.net/2117/352053 https://dx.doi.org/10.1007/s12346-021-00486-6 |
| Access Level: | acceso abierto |
| Palabra clave: | Many-body problem Celestial mechanics Five-body problem Central configuration Rhombus configuration Square configuration Problema dels cossos múltiples Mecànica celest Classificació AMS::37 Dynamical systems and ergodic theory::37N Applications Classificació AMS::70 Mechanics of particles and systems::70F Dynamics of a system of particles, including celestial mechanics Àrees temàtiques de la UPC::Matemàtiques i estadística Àrees temàtiques de la UPC::Enginyeria mecànica |
| Sumario: | We show the existence of central configurations in the planar five-body problem where four bodies are located at the vertices of a rhombus, called rhombus plus one central configurations. Concretely we prove analytically their existence when one diagonal is nearly equal to the sides of the rhombus and when the two diagonals are either equal or nearly equal. In addition, we prove that given a rhombus plus one configuration, the corresponding vector of positive masses that makes the configuration central, if exists, is unique. |
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