On the equilateral pentagonal central configurations

An equilateral pentagon is a polygon in the plane with five sides of equal length. In this paper we classify the central configurations of the 5-body problem having the five bodies at the vertices of an equilateral pentagon with an axis of symmetry. We prove that there are two unique classes of such...

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Bibliographic Details
Authors: Alvarez-Ramírez, M., Gasull, A., Llibre, J.
Format: article
Status:Versión aceptada para publicación
Publication Date:2022
Country:España
Institution:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repository:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2072/535412
Online Access:http://hdl.handle.net/2072/535412
Access Level:Open access
Keyword:5-body problem
Central configuration
Equilateral pentagon
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spelling On the equilateral pentagonal central configurationsAlvarez-Ramírez, M.Gasull, A.Llibre, J.5-body problemCentral configurationEquilateral pentagonAn equilateral pentagon is a polygon in the plane with five sides of equal length. In this paper we classify the central configurations of the 5-body problem having the five bodies at the vertices of an equilateral pentagon with an axis of symmetry. We prove that there are two unique classes of such equilateral pentagons providing central configurations, one concave equilateral pentagon and one convex equilateral pentagon, the regular one. A key point of our proof is the use of rational parameterizations to transform the corresponding equations, which involve square roots, into polynomial equations. © 2022 Elsevier B.V.The first author is partially supported by the grant Sistemas Hamiltonianos, Mecánica y Geometría from the PAPDI2021 CBI-UAMI . The second author is partially supported by the grant Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D ( CEX2020-001084-M ). The last two authors are partially by the Agencia Estatal de Investigación grant PID2019-104658GB-I00 , and the H2020 European Research Council grant MSCA-RISE-2017-777911 .Elsevier B.V.2022info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersion19 p.application/pdfhttp://hdl.handle.net/2072/535412RECERCAT (Dipòsit de la Recerca de Catalunya)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésCommunications in Nonlinear Science and Numerical Simulationinfo:eu-repo/semantics/openAccessoai:recercat.cat:2072/5354122026-05-29T05:05:01Z
dc.title.none.fl_str_mv On the equilateral pentagonal central configurations
title On the equilateral pentagonal central configurations
spellingShingle On the equilateral pentagonal central configurations
Alvarez-Ramírez, M.
5-body problem
Central configuration
Equilateral pentagon
title_short On the equilateral pentagonal central configurations
title_full On the equilateral pentagonal central configurations
title_fullStr On the equilateral pentagonal central configurations
title_full_unstemmed On the equilateral pentagonal central configurations
title_sort On the equilateral pentagonal central configurations
dc.creator.none.fl_str_mv Alvarez-Ramírez, M.
Gasull, A.
Llibre, J.
author Alvarez-Ramírez, M.
author_facet Alvarez-Ramírez, M.
Gasull, A.
Llibre, J.
author_role author
author2 Gasull, A.
Llibre, J.
author2_role author
author
dc.subject.none.fl_str_mv 5-body problem
Central configuration
Equilateral pentagon
topic 5-body problem
Central configuration
Equilateral pentagon
description An equilateral pentagon is a polygon in the plane with five sides of equal length. In this paper we classify the central configurations of the 5-body problem having the five bodies at the vertices of an equilateral pentagon with an axis of symmetry. We prove that there are two unique classes of such equilateral pentagons providing central configurations, one concave equilateral pentagon and one convex equilateral pentagon, the regular one. A key point of our proof is the use of rational parameterizations to transform the corresponding equations, which involve square roots, into polynomial equations. © 2022 Elsevier B.V.
publishDate 2022
dc.date.none.fl_str_mv 2022
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/2072/535412
url http://hdl.handle.net/2072/535412
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Communications in Nonlinear Science and Numerical Simulation
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 19 p.
application/pdf
dc.publisher.none.fl_str_mv Elsevier B.V.
publisher.none.fl_str_mv Elsevier B.V.
dc.source.none.fl_str_mv RECERCAT (Dipòsit de la Recerca de Catalunya)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.812429

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