Two helpful developments towards better understanding 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: | 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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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 |
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info:eu-repo/semantics/openAccess |
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openAccess |
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application/pdf |
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Universidade Federal de Minas Gerais |
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UFMG |
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Brasil |
dc.publisher.department.fl_str_mv |
ICX - DEPARTAMENTO DE FÍSICA |
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Universidade Federal de Minas Gerais |
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