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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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
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spelling On Nested Central Configurations of the 3n Body ProblemBarrabés Vera, Esther|||0000-0002-8448-692XCors Iglesias, Josep Maria|||0000-0002-9803-8490Fernandes, Antonio Carlos|||0000-0001-9297-5101Vidal, Claudio|||0000-0002-1630-0898Celestial mechanicsN-body problemPlanar central configurationsHomographic solutionNested central configurationsIn 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. 220252025-01-0120262026-08-31Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articlehttps://ddd.uab.cat/record/318291https://dx.doi.org/urn:doi:10.1007/s00332-025-10162-7reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengAgencia Estatal de Investigación https://doi.org/10.13039/501100011033 PID2021-123968NB-I00Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 PID2022-136613NB-I00embargoed accesshttp://purl.org/coar/access_right/c_f1cfAquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/embargoedAccessoai:ddd.uab.cat:3182912026-06-06T12:50:31Z
dc.title.none.fl_str_mv On Nested Central Configurations of the 3n Body Problem
title On Nested Central Configurations of the 3n Body Problem
spellingShingle On Nested Central Configurations of the 3n Body Problem
Barrabés Vera, Esther|||0000-0002-8448-692X
Celestial mechanics
N-body problem
Planar central configurations
Homographic solution
Nested central configurations
title_short On Nested Central Configurations of the 3n Body Problem
title_full On Nested Central Configurations of the 3n Body Problem
title_fullStr On Nested Central Configurations of the 3n Body Problem
title_full_unstemmed On Nested Central Configurations of the 3n Body Problem
title_sort On Nested Central Configurations of the 3n Body Problem
dc.creator.none.fl_str_mv 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
author Barrabés Vera, Esther|||0000-0002-8448-692X
author_facet 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
author_role author
author2 Cors Iglesias, Josep Maria|||0000-0002-9803-8490
Fernandes, Antonio Carlos|||0000-0001-9297-5101
Vidal, Claudio|||0000-0002-1630-0898
author2_role author
author
author
dc.subject.none.fl_str_mv Celestial mechanics
N-body problem
Planar central configurations
Homographic solution
Nested central configurations
topic Celestial mechanics
N-body problem
Planar central configurations
Homographic solution
Nested central configurations
description 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.
publishDate 2025
dc.date.none.fl_str_mv
2
2025
2025-01-01
2026
2026-08-31
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
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dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/318291
https://dx.doi.org/urn:doi:10.1007/s00332-025-10162-7
url https://ddd.uab.cat/record/318291
https://dx.doi.org/urn:doi:10.1007/s00332-025-10162-7
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 PID2021-123968NB-I00
Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 PID2022-136613NB-I00
dc.rights.none.fl_str_mv embargoed access
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dc.rights.openaire.fl_str_mv info:eu-repo/semantics/embargoedAccess
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dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
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