Two helpful developments towards better understanding adiabatic invariance in classical mechanics

Detalhes bibliográficos
Autor(a) principal: José Rachid Mohallem
Data de Publicação: 2019
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UFMG
Texto Completo: http://dx.doi.org/10.1590/1806-9126-RBEF-2018-0214
http://hdl.handle.net/1843/36978
https://orcid.org/0000-0002-4776-4417
Resumo: CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico
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spelling 2021-07-26T19:48:43Z2021-07-26T19:48:43Z2019412e20180214e20180214-4http://dx.doi.org/10.1590/1806-9126-RBEF-2018-02141806-9126http://hdl.handle.net/1843/36978https://orcid.org/0000-0002-4776-4417CNPq - Conselho Nacional de Desenvolvimento Científico e TecnológicoThe 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.engUniversidade Federal de Minas GeraisUFMGBrasilICX - DEPARTAMENTO DE FÍSICARevista brasileira de ensino de físicaMecânica clássicaEnergiaAdiabatic invarianceClassical mechanicsGraduate teachingTwo helpful developments towards better understanding adiabatic invariance in classical mechanicsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttps://www.scielo.br/j/rbef/a/3nsD9gRzC6zWpJRPMKqrMby/?format=pdf&lang=enJosé Rachid Mohallemapplication/pdfinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFMGinstname:Universidade Federal de Minas Gerais (UFMG)instacron:UFMGORIGINALTwo helpful developments towards better understanding of.pdfTwo helpful developments towards better understanding of.pdfapplication/pdf205359https://repositorio.ufmg.br/bitstream/1843/36978/2/Two%20helpful%20developments%20towards%20better%20understanding%20of.pdf06454ea605550147fd1d8e68cac02946MD52LICENSELicense.txtLicense.txttext/plain; charset=utf-82042https://repositorio.ufmg.br/bitstream/1843/36978/1/License.txtfa505098d172de0bc8864fc1287ffe22MD511843/369782021-08-03 16:34:33.911oai:repositorio.ufmg.br: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Repositório de PublicaçõesPUBhttps://repositorio.ufmg.br/oaiopendoar:2021-08-03T19:34:33Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)false
dc.title.pt_BR.fl_str_mv Two helpful developments towards better understanding adiabatic invariance in classical mechanics
title Two helpful developments towards better understanding adiabatic invariance in classical mechanics
spellingShingle Two helpful developments towards better understanding adiabatic invariance in classical mechanics
José Rachid Mohallem
Adiabatic invariance
Classical mechanics
Graduate teaching
Mecânica clássica
Energia
title_short Two helpful developments towards better understanding adiabatic invariance in classical mechanics
title_full Two helpful developments towards better understanding adiabatic invariance in classical mechanics
title_fullStr Two helpful developments towards better understanding adiabatic invariance in classical mechanics
title_full_unstemmed Two helpful developments towards better understanding adiabatic invariance in classical mechanics
title_sort Two helpful developments towards better understanding adiabatic invariance in classical mechanics
author José Rachid Mohallem
author_facet José Rachid Mohallem
author_role author
dc.contributor.author.fl_str_mv José Rachid Mohallem
dc.subject.por.fl_str_mv Adiabatic invariance
Classical mechanics
Graduate teaching
topic Adiabatic invariance
Classical mechanics
Graduate teaching
Mecânica clássica
Energia
dc.subject.other.pt_BR.fl_str_mv Mecânica clássica
Energia
description CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico
publishDate 2019
dc.date.issued.fl_str_mv 2019
dc.date.accessioned.fl_str_mv 2021-07-26T19:48:43Z
dc.date.available.fl_str_mv 2021-07-26T19:48:43Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/1843/36978
dc.identifier.doi.pt_BR.fl_str_mv http://dx.doi.org/10.1590/1806-9126-RBEF-2018-0214
dc.identifier.issn.pt_BR.fl_str_mv 1806-9126
dc.identifier.orcid.pt_BR.fl_str_mv https://orcid.org/0000-0002-4776-4417
url http://dx.doi.org/10.1590/1806-9126-RBEF-2018-0214
http://hdl.handle.net/1843/36978
https://orcid.org/0000-0002-4776-4417
identifier_str_mv 1806-9126
dc.language.iso.fl_str_mv eng
language eng
dc.relation.ispartof.pt_BR.fl_str_mv Revista brasileira de ensino de física
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universidade Federal de Minas Gerais
dc.publisher.initials.fl_str_mv UFMG
dc.publisher.country.fl_str_mv Brasil
dc.publisher.department.fl_str_mv ICX - DEPARTAMENTO DE FÍSICA
publisher.none.fl_str_mv Universidade Federal de Minas Gerais
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFMG
instname:Universidade Federal de Minas Gerais (UFMG)
instacron:UFMG
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