On the convex central configurations of the symmetric (ℓ + 2)-body problem

For the 4-body problem there is the following conjecture: Given arbitrary positive masses, the planar 4-body problem has a unique convex central configuration for each ordering of the masses on its convex hull. Until now this conjecture has remained open. Our aim is to prove that this conjecture can...

Descripción completa

Detalles Bibliográficos
Autores: Corbera Subirana, Montserrat|||0000-0002-0367-9667, Llibre, Jaume|||0000-0002-9511-5999, Yuan, Pengfei
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:228116
Acceso en línea:https://ddd.uab.cat/record/228116
https://dx.doi.org/urn:doi:10.1134/S1560354720030028
Access Level:acceso abierto
Palabra clave:Convex central configurations
(ℓ + 2)-body problem
id ES_84b9386597ffd9c19ad0afc386738773
oai_identifier_str oai:ddd.uab.cat:228116
network_acronym_str ES
network_name_str España
repository_id_str
spelling On the convex central configurations of the symmetric (ℓ + 2)-body problemCorbera Subirana, Montserrat|||0000-0002-0367-9667Llibre, Jaume|||0000-0002-9511-5999Yuan, PengfeiConvex central configurations(ℓ + 2)-body problemFor the 4-body problem there is the following conjecture: Given arbitrary positive masses, the planar 4-body problem has a unique convex central configuration for each ordering of the masses on its convex hull. Until now this conjecture has remained open. Our aim is to prove that this conjecture cannot be extended to the (ℓ + 2)-body problem with ℓ ⩾ 3. In particular, we prove that the symmetric (2n + 1)-body problem with masses m1 = … = m2n-1 = 1 and m2n = m2n+1 = m sufficiently small has at least two classes of convex central configuration when n = 2, five when n = 3, and four when n = 4. We conjecture that the (2n + 1)-body problem has at least n classes of convex central configurations for n > 4 and we give some numerical evidence that the conjecture can be true. We also prove that the symmetric (2n + 2)-body problem with masses m1 = … = m2n = 1 and m2n+1 = m2n+2 = m sufficiently small has at least three classes of convex central configuration when n = 3, two when n = 4, and three when n = 5. We also conjecture that the (2n + 2)-body problem has at least [(n +1)/2] classes of convex central configurations for n > 5 and we give some numerical evidences that the conjecture can be true. 22020-01-0120202020-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/228116https://dx.doi.org/urn:doi:10.1134/S1560354720030028reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2016-77278-PAgència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1617European Commission https://doi.org/10.13039/501100000780 777911open accesshttp://purl.org/coar/access_right/c_abf2Aquest 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/openAccessoai:ddd.uab.cat:2281162026-06-06T12:50:31Z
dc.title.none.fl_str_mv On the convex central configurations of the symmetric (ℓ + 2)-body problem
title On the convex central configurations of the symmetric (ℓ + 2)-body problem
spellingShingle On the convex central configurations of the symmetric (ℓ + 2)-body problem
Corbera Subirana, Montserrat|||0000-0002-0367-9667
Convex central configurations
(ℓ + 2)-body problem
title_short On the convex central configurations of the symmetric (ℓ + 2)-body problem
title_full On the convex central configurations of the symmetric (ℓ + 2)-body problem
title_fullStr On the convex central configurations of the symmetric (ℓ + 2)-body problem
title_full_unstemmed On the convex central configurations of the symmetric (ℓ + 2)-body problem
title_sort On the convex central configurations of the symmetric (ℓ + 2)-body problem
dc.creator.none.fl_str_mv Corbera Subirana, Montserrat|||0000-0002-0367-9667
Llibre, Jaume|||0000-0002-9511-5999
Yuan, Pengfei
author Corbera Subirana, Montserrat|||0000-0002-0367-9667
author_facet Corbera Subirana, Montserrat|||0000-0002-0367-9667
Llibre, Jaume|||0000-0002-9511-5999
Yuan, Pengfei
author_role author
author2 Llibre, Jaume|||0000-0002-9511-5999
Yuan, Pengfei
author2_role author
author
dc.subject.none.fl_str_mv Convex central configurations
(ℓ + 2)-body problem
topic Convex central configurations
(ℓ + 2)-body problem
description For the 4-body problem there is the following conjecture: Given arbitrary positive masses, the planar 4-body problem has a unique convex central configuration for each ordering of the masses on its convex hull. Until now this conjecture has remained open. Our aim is to prove that this conjecture cannot be extended to the (ℓ + 2)-body problem with ℓ ⩾ 3. In particular, we prove that the symmetric (2n + 1)-body problem with masses m1 = … = m2n-1 = 1 and m2n = m2n+1 = m sufficiently small has at least two classes of convex central configuration when n = 2, five when n = 3, and four when n = 4. We conjecture that the (2n + 1)-body problem has at least n classes of convex central configurations for n > 4 and we give some numerical evidence that the conjecture can be true. We also prove that the symmetric (2n + 2)-body problem with masses m1 = … = m2n = 1 and m2n+1 = m2n+2 = m sufficiently small has at least three classes of convex central configuration when n = 3, two when n = 4, and three when n = 5. We also conjecture that the (2n + 2)-body problem has at least [(n +1)/2] classes of convex central configurations for n > 5 and we give some numerical evidences that the conjecture can be true.
publishDate 2020
dc.date.none.fl_str_mv 2
2020-01-01
2020
2020-01-01
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
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/228116
https://dx.doi.org/urn:doi:10.1134/S1560354720030028
url https://ddd.uab.cat/record/228116
https://dx.doi.org/urn:doi:10.1134/S1560354720030028
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2016-77278-P
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1617
European Commission https://doi.org/10.13039/501100000780 777911
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
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
collection Dipòsit Digital de Documents de la UAB
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869412245828534272
score 15,300724

Similares en LA Referencia