Two helpful developments towards better understanding of adiabatic invariance in classical mechanics
Autor(a) principal: | |
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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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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 |
format |
article |
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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1752122423986094080 |