On Nested Central Configurations of the 3n Body Problem

In this work, we consider the existence of (3, n)-crowns in the classical Newtonian 3n-body problem, which are central configurations formed by three groups of n bodies with the same mass within each group, located at the vertices of three concentric regular polygons. We consider the case with dihed...

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Detalles Bibliográficos
Autores: Barrabés Vera, Esther|||0000-0002-8448-692X, Cors Iglesias, Josep Maria|||0000-0002-9803-8490, Fernandes, Antonio Carlos|||0000-0001-9297-5101, Vidal, Claudio|||0000-0002-1630-0898
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:318291
Acceso en línea:https://ddd.uab.cat/record/318291
https://dx.doi.org/urn:doi:10.1007/s00332-025-10162-7
Access Level:acceso embargado
Palabra clave:Celestial mechanics
N-body problem
Planar central configurations
Homographic solution
Nested central configurations
Descripción
Sumario:In this work, we consider the existence of (3, n)-crowns in the classical Newtonian 3n-body problem, which are central configurations formed by three groups of n bodies with the same mass within each group, located at the vertices of three concentric regular polygons. We consider the case with dihedral symmetry, called nested (3, n)-crowns, where the vertices of the polygons are aligned. We characterize the set of admissible radii for the polygons for which nested (3, n)-crowns exist. We conclude with numerical evidences that suggest uniqueness for each set of three masses.