Convexity and symmetry of central configurations in the five-body problem: Lagrange plus two
We study convexity and symmetry of central configurations in the five body problem when three of the masses ara located at the vertices of an equilateral triangle, that we call Lagrange plus two central configurations. First, we prove that the two bodies out of the vertices of the triangle cannot be...
| Autores: | , , , |
|---|---|
| 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:2117/355962 |
| Acceso en línea: | https://hdl.handle.net/2117/355962 https://dx.doi.org/10.1007/s12346-021-00504-7 |
| Access Level: | acceso abierto |
| Palabra clave: | Many-body problem Configurations Lagrange problem Problema dels cossos múltiples Classificació AMS::70 Mechanics of particles and systems::70F Dynamics of a system of particles, including celestial mechanics Àrees temàtiques de la UPC::Enginyeria mecànica Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | We study convexity and symmetry of central configurations in the five body problem when three of the masses ara located at the vertices of an equilateral triangle, that we call Lagrange plus two central configurations. First, we prove that the two bodies out of the vertices of the triangle cannot be placed on certain lines. Next, we give a geometrical characterization of such configurations in the sense as that of Dziobek, and we describe the admissible regions where the two remaining bodies can be placed. Furthermore, we prove that any Lagrange plus two central configuration is concave. Finally, we show numerically the existence of non-symmetric central configurations of the five body problem. |
|---|