On central configurations of the kn-body problem
We consider planar central configurations of the Newtonian kn-body problem consisting in k groups of regular n-gons of equal masses, called (k, n)-crown. We derive the equations of central configurations for a general (k, n)-crown. When k = 2 we prove the existence of a twisted (2, n)-crown for any...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2019 |
| 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:2117/132982 |
| Acceso en línea: | https://hdl.handle.net/2117/132982 https://dx.doi.org/10.1016/j.jmaa.2019.04.010 |
| Access Level: | acceso abierto |
| Palabra clave: | Celestial mechanics Many-body problem N-body problem Planar central configurations Twisted central configurations Mecànica celest 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::Matemàtiques i estadística |
| Sumario: | We consider planar central configurations of the Newtonian kn-body problem consisting in k groups of regular n-gons of equal masses, called (k, n)-crown. We derive the equations of central configurations for a general (k, n)-crown. When k = 2 we prove the existence of a twisted (2, n)-crown for any value of the mass ratio. Moreover, for n = 3,4 and any value of the mass ratio, we give the exact number of twisted (2, n)-crowns, and describe their location. Finally, we conjecture that for any value of the mass ratio there exist exactly three (2, n)-crowns for n = 5. |
|---|