The 3-dimensional cored and logarithm potencials: Periodic orits

We study analytically families of periodic orbits for the cored and logarithmic Hamiltonians H(x, y, z, px, py, pz) = (p2x +p2y +p2z/q)/2+ (1+x2 +(y2 +z2)/q2)1/2, and H(x, y, z, px, py, pz) = (p2x +p2y +p2z/q)/2+ (log(1+x2 +(y2 + z2)/q2))/2, with 3 degrees of freedom, which are relevant in the analy...

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Detalles Bibliográficos
Autores: Kulesza, Maite, Llibre, Jaume|||0000-0002-9511-5999
Tipo de recurso: artículo
Fecha de publicación:2014
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:150729
Acceso en línea:https://ddd.uab.cat/record/150729
https://dx.doi.org/urn:doi:10.1063/1.4901126
Access Level:acceso abierto
Palabra clave:Periodic orbits
Galactic potential
Cored potential
Logarithm potential
Averaging theory
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spelling The 3-dimensional cored and logarithm potencials: Periodic oritsKulesza, MaiteLlibre, Jaume|||0000-0002-9511-5999Periodic orbitsGalactic potentialCored potentialLogarithm potentialAveraging theoryWe study analytically families of periodic orbits for the cored and logarithmic Hamiltonians H(x, y, z, px, py, pz) = (p2x +p2y +p2z/q)/2+ (1+x2 +(y2 +z2)/q2)1/2, and H(x, y, z, px, py, pz) = (p2x +p2y +p2z/q)/2+ (log(1+x2 +(y2 + z2)/q2))/2, with 3 degrees of freedom, which are relevant in the analysis of the galactic dynamics. First, after introducing a scale transformation in the coordinates and momenta with a parameter ε, we show that both systems give essentially the same set of equations of motion up to first order in ε. Then the conditions for finding families of periodic orbits, using the averaging theory up to first order in ε, apply equally to both systems in every energy level H = h > 0. The averaging method used proves the existence of at most three periodic orbits, for ε small enough, and gives an analytic approximation for the initial conditions of these periodic orbits. 22014-01-0120142014-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/150729https://dx.doi.org/urn:doi:10.1063/1.4901126reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2008-03437Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2009/SGR-410European Commission https://doi.org/10.13039/501100000780 318999European Commission https://doi.org/10.13039/501100000780 316338open 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:1507292026-06-06T12:50:31Z
dc.title.none.fl_str_mv The 3-dimensional cored and logarithm potencials: Periodic orits
title The 3-dimensional cored and logarithm potencials: Periodic orits
spellingShingle The 3-dimensional cored and logarithm potencials: Periodic orits
Kulesza, Maite
Periodic orbits
Galactic potential
Cored potential
Logarithm potential
Averaging theory
title_short The 3-dimensional cored and logarithm potencials: Periodic orits
title_full The 3-dimensional cored and logarithm potencials: Periodic orits
title_fullStr The 3-dimensional cored and logarithm potencials: Periodic orits
title_full_unstemmed The 3-dimensional cored and logarithm potencials: Periodic orits
title_sort The 3-dimensional cored and logarithm potencials: Periodic orits
dc.creator.none.fl_str_mv Kulesza, Maite
Llibre, Jaume|||0000-0002-9511-5999
author Kulesza, Maite
author_facet Kulesza, Maite
Llibre, Jaume|||0000-0002-9511-5999
author_role author
author2 Llibre, Jaume|||0000-0002-9511-5999
author2_role author
dc.subject.none.fl_str_mv Periodic orbits
Galactic potential
Cored potential
Logarithm potential
Averaging theory
topic Periodic orbits
Galactic potential
Cored potential
Logarithm potential
Averaging theory
description We study analytically families of periodic orbits for the cored and logarithmic Hamiltonians H(x, y, z, px, py, pz) = (p2x +p2y +p2z/q)/2+ (1+x2 +(y2 +z2)/q2)1/2, and H(x, y, z, px, py, pz) = (p2x +p2y +p2z/q)/2+ (log(1+x2 +(y2 + z2)/q2))/2, with 3 degrees of freedom, which are relevant in the analysis of the galactic dynamics. First, after introducing a scale transformation in the coordinates and momenta with a parameter ε, we show that both systems give essentially the same set of equations of motion up to first order in ε. Then the conditions for finding families of periodic orbits, using the averaging theory up to first order in ε, apply equally to both systems in every energy level H = h > 0. The averaging method used proves the existence of at most three periodic orbits, for ε small enough, and gives an analytic approximation for the initial conditions of these periodic orbits.
publishDate 2014
dc.date.none.fl_str_mv 2
2014-01-01
2014
2014-01-01
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/150729
https://dx.doi.org/urn:doi:10.1063/1.4901126
url https://ddd.uab.cat/record/150729
https://dx.doi.org/urn:doi:10.1063/1.4901126
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2008-03437
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2009/SGR-410
European Commission https://doi.org/10.13039/501100000780 318999
European Commission https://doi.org/10.13039/501100000780 316338
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
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