On Nested Central Configurations of the 3n Body Problem
Barrabés Vera, Esther (Universitat de Girona)
Cors Iglesias, Josep Maria (Universitat Politècnica de Catalunya)
Fernandes, Antonio Carlos (Universidade Federal de Itajubá. Instituto de Matemática e Computação)
Vidal, Claudio (Universidad del Bío-Bío. Departamento de Matemática)

Date:	2025
Abstract:	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.
Grants:	Agencia Estatal de Investigación PID2021-123968NB-I00 Agencia Estatal de Investigación PID2022-136613NB-I00
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Celestial mechanics ; N-body problem ; Planar central configurations ; Homographic solution ; Nested central configurations
Published in:	Journal of Nonlinear Science, Vol. 35, Issue 4 (August 2025) , art. 67, ISSN 1432-1467

DOI: 10.1007/s00332-025-10162-7

Available from: 2026-08-31 Postprint

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
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