Two helpful developments towards better understanding of adiabatic invariance in classical mechanics

Detalhes bibliográficos
Autor(a) principal: Mohallem,J.R.
Data de Publicação: 2019
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Revista Brasileira de Ensino de Física (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172019000200402
Resumo: Abstract The topic of difficult understanding of adiabatic invariance in classical mechanics is dealt with in a more understandable way. Using the one-dimensional harmonic oscillator as an example, the goals of this paper are twofold. First, given a first-order parameter variation, the second-order magnitude of the correction to the adiabatic invariant is established in simple terms. Second, the identification of the action variable with the invariant quantity for slow variations of different parameters of the Hamiltonian is confirmed, by invoking the correct equation of motion in the derivation.
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spelling Two helpful developments towards better understanding of adiabatic invariance in classical mechanicsAdiabatic invariantclassical mechanicsAbstract The topic of difficult understanding of adiabatic invariance in classical mechanics is dealt with in a more understandable way. Using the one-dimensional harmonic oscillator as an example, the goals of this paper are twofold. First, given a first-order parameter variation, the second-order magnitude of the correction to the adiabatic invariant is established in simple terms. Second, the identification of the action variable with the invariant quantity for slow variations of different parameters of the Hamiltonian is confirmed, by invoking the correct equation of motion in the derivation.Sociedade Brasileira de Física2019-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172019000200402Revista Brasileira de Ensino de Física v.41 n.2 2019reponame:Revista Brasileira de Ensino de Física (Online)instname:Sociedade Brasileira de Física (SBF)instacron:SBF10.1590/1806-9126-rbef-2018-0214info:eu-repo/semantics/openAccessMohallem,J.R.eng2018-09-18T00:00:00Zoai:scielo:S1806-11172019000200402Revistahttp://www.sbfisica.org.br/rbef/https://old.scielo.br/oai/scielo-oai.php||marcio@sbfisica.org.br1806-91261806-1117opendoar:2018-09-18T00:00Revista Brasileira de Ensino de Física (Online) - Sociedade Brasileira de Física (SBF)false
dc.title.none.fl_str_mv Two helpful developments towards better understanding of adiabatic invariance in classical mechanics
title Two helpful developments towards better understanding of adiabatic invariance in classical mechanics
spellingShingle Two helpful developments towards better understanding of adiabatic invariance in classical mechanics
Mohallem,J.R.
Adiabatic invariant
classical mechanics
title_short Two helpful developments towards better understanding of adiabatic invariance in classical mechanics
title_full Two helpful developments towards better understanding of adiabatic invariance in classical mechanics
title_fullStr Two helpful developments towards better understanding of adiabatic invariance in classical mechanics
title_full_unstemmed Two helpful developments towards better understanding of adiabatic invariance in classical mechanics
title_sort Two helpful developments towards better understanding of adiabatic invariance in classical mechanics
author Mohallem,J.R.
author_facet Mohallem,J.R.
author_role author
dc.contributor.author.fl_str_mv Mohallem,J.R.
dc.subject.por.fl_str_mv Adiabatic invariant
classical mechanics
topic Adiabatic invariant
classical mechanics
description Abstract The topic of difficult understanding of adiabatic invariance in classical mechanics is dealt with in a more understandable way. Using the one-dimensional harmonic oscillator as an example, the goals of this paper are twofold. First, given a first-order parameter variation, the second-order magnitude of the correction to the adiabatic invariant is established in simple terms. Second, the identification of the action variable with the invariant quantity for slow variations of different parameters of the Hamiltonian is confirmed, by invoking the correct equation of motion in the derivation.
publishDate 2019
dc.date.none.fl_str_mv 2019-01-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172019000200402
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172019000200402
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/1806-9126-rbef-2018-0214
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Física
publisher.none.fl_str_mv Sociedade Brasileira de Física
dc.source.none.fl_str_mv Revista Brasileira de Ensino de Física v.41 n.2 2019
reponame:Revista Brasileira de Ensino de Física (Online)
instname:Sociedade Brasileira de Física (SBF)
instacron:SBF
instname_str Sociedade Brasileira de Física (SBF)
instacron_str SBF
institution SBF
reponame_str Revista Brasileira de Ensino de Física (Online)
collection Revista Brasileira de Ensino de Física (Online)
repository.name.fl_str_mv Revista Brasileira de Ensino de Física (Online) - Sociedade Brasileira de Física (SBF)
repository.mail.fl_str_mv ||marcio@sbfisica.org.br
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