Uniqueness results for co-circular central configurations for power-law potentials

For a class of potential functions including those used for the planar n-body and n-vortex problems, we investigate co-circular central configurations whose center of mass coincides with the center of the circle containing the bodies. Useful equations are derived that completely describe the problem...

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Detalles Bibliográficos
Autores: Cors Iglesias, Josep Maria|||0000-0002-9803-8490, Hall, Glen Richard, Roberts, Gareth E.
Tipo de recurso: artículo
Fecha de publicación:2014
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:150681
Acceso en línea:https://ddd.uab.cat/record/150681
https://dx.doi.org/urn:doi:10.1016/j.physd.2014.05.003
Access Level:acceso abierto
Palabra clave:Central configuration
N-body problem
N-vortex problem
Co-circular central configuration
Descripción
Sumario:For a class of potential functions including those used for the planar n-body and n-vortex problems, we investigate co-circular central configurations whose center of mass coincides with the center of the circle containing the bodies. Useful equations are derived that completely describe the problem. Using a topological approach, it is shown that for any choice of positive masses (or circulations), if such a central configuration exists, then it is unique. It quickly follows that if the masses are all equal, then the only solution is the regular n-gon. For the planar n-vortex problem and any choice of the vorticities, we show that the only possible cocircular central configuration with center of vorticity at the center of the circle is the regular n-gon with equal vorticities.