The divergence and curl in arbitrary basis

In this work, the divergence and curl operators are obtained using the coordinate free non rigid basis formulation of differential geometry. Although the authors have attempted to keep the presentation self-contained as much as possible, some previous exposure to the language of differential geometr...

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Detalles Bibliográficos
Autores: Medeiros, Waleska Priscylla Florencio de, Lima, Rodrigo Ramos de, Andrade, Vanessa Carvalho de, Müller, Daniel
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2019
País:Brasil
Institución:Universidade de Brasília (UnB)
Repositorio:Repositório Institucional da UnB
Idioma:inglés
OAI Identifier:oai:repositorio.unb.br:10482/36550
Acceso en línea:https://repositorio.unb.br/handle/10482/36550
https://doi.org/10.1590/1806-9126-rbef-2018-0082
http://orcid.org/0000-0003-4650-5947
Access Level:acceso abierto
Palabra clave:Cálculo vetorial
Geometria diferencial
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spelling The divergence and curl in arbitrary basisCálculo vetorialGeometria diferencialIn this work, the divergence and curl operators are obtained using the coordinate free non rigid basis formulation of differential geometry. Although the authors have attempted to keep the presentation self-contained as much as possible, some previous exposure to the language of differential geometry may be helpful. In this sense the work is aimed to late undergraduate or beginners graduate students interested in mathematical physics. To illustrate the development, we graphically present the eleven coordinate systems in which the Laplace operator is separable. We detail the development of the basis and the connection for the cylindrical and paraboloidal coordinate systems. We also present in [1] codes both in Maxima and Maple for the spherical orthonormal basis, which serves as a working model for calculations in other situations of interest. Also in [1] the codes to obtain the coordinate surfaces are given.Sociedade Brasileira de Física2020-01-24T10:31:46Z2020-01-24T10:31:46Z2019info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfMEDEIROS, Waleska Priscylla Florencio de et al. The divergence and curl in arbitrary basis. Revista Brasileira de Ensino de Física, v. 41, n. 2, e20180082, 2019. DOI: https://doi.org/10.1590/1806-9126-rbef-2018-0082. Disponível em: http://scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172019000200413. Acesso em: 23 jan. 2020.https://repositorio.unb.br/handle/10482/36550https://doi.org/10.1590/1806-9126-rbef-2018-0082http://orcid.org/0000-0003-4650-5947(CC BY) - Licença Creative Commonsinfo:eu-repo/semantics/openAccessengreponame:Repositório Institucional da UnBinstname:Universidade de Brasília (UnB)instacron:UNBMedeiros, Waleska Priscylla Florencio deLima, Rodrigo Ramos deAndrade, Vanessa Carvalho deMüller, Daniel2023-05-27T00:19:55Zoai:repositorio.unb.br:10482/36550Repositório InstitucionalPUBhttps://repositorio.unb.br/oai/requestrepositorio@unb.bropendoar:2023-05-27T00:19:55Repositório Institucional da UnB - Universidade de Brasília (UnB)false
dc.title.none.fl_str_mv The divergence and curl in arbitrary basis
title The divergence and curl in arbitrary basis
spellingShingle The divergence and curl in arbitrary basis
Medeiros, Waleska Priscylla Florencio de
Cálculo vetorial
Geometria diferencial
title_short The divergence and curl in arbitrary basis
title_full The divergence and curl in arbitrary basis
title_fullStr The divergence and curl in arbitrary basis
title_full_unstemmed The divergence and curl in arbitrary basis
title_sort The divergence and curl in arbitrary basis
dc.creator.none.fl_str_mv Medeiros, Waleska Priscylla Florencio de
Lima, Rodrigo Ramos de
Andrade, Vanessa Carvalho de
Müller, Daniel
author Medeiros, Waleska Priscylla Florencio de
author_facet Medeiros, Waleska Priscylla Florencio de
Lima, Rodrigo Ramos de
Andrade, Vanessa Carvalho de
Müller, Daniel
author_role author
author2 Lima, Rodrigo Ramos de
Andrade, Vanessa Carvalho de
Müller, Daniel
author2_role author
author
author
dc.subject.por.fl_str_mv Cálculo vetorial
Geometria diferencial
topic Cálculo vetorial
Geometria diferencial
description In this work, the divergence and curl operators are obtained using the coordinate free non rigid basis formulation of differential geometry. Although the authors have attempted to keep the presentation self-contained as much as possible, some previous exposure to the language of differential geometry may be helpful. In this sense the work is aimed to late undergraduate or beginners graduate students interested in mathematical physics. To illustrate the development, we graphically present the eleven coordinate systems in which the Laplace operator is separable. We detail the development of the basis and the connection for the cylindrical and paraboloidal coordinate systems. We also present in [1] codes both in Maxima and Maple for the spherical orthonormal basis, which serves as a working model for calculations in other situations of interest. Also in [1] the codes to obtain the coordinate surfaces are given.
publishDate 2019
dc.date.none.fl_str_mv 2019
2020-01-24T10:31:46Z
2020-01-24T10:31:46Z
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 MEDEIROS, Waleska Priscylla Florencio de et al. The divergence and curl in arbitrary basis. Revista Brasileira de Ensino de Física, v. 41, n. 2, e20180082, 2019. DOI: https://doi.org/10.1590/1806-9126-rbef-2018-0082. Disponível em: http://scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172019000200413. Acesso em: 23 jan. 2020.
https://repositorio.unb.br/handle/10482/36550
https://doi.org/10.1590/1806-9126-rbef-2018-0082
http://orcid.org/0000-0003-4650-5947
identifier_str_mv MEDEIROS, Waleska Priscylla Florencio de et al. The divergence and curl in arbitrary basis. Revista Brasileira de Ensino de Física, v. 41, n. 2, e20180082, 2019. DOI: https://doi.org/10.1590/1806-9126-rbef-2018-0082. Disponível em: http://scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172019000200413. Acesso em: 23 jan. 2020.
url https://repositorio.unb.br/handle/10482/36550
https://doi.org/10.1590/1806-9126-rbef-2018-0082
http://orcid.org/0000-0003-4650-5947
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv (CC BY) - Licença Creative Commons
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (CC BY) - Licença Creative Commons
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
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 reponame:Repositório Institucional da UnB
instname:Universidade de Brasília (UnB)
instacron:UNB
instname_str Universidade de Brasília (UnB)
instacron_str UNB
institution UNB
reponame_str Repositório Institucional da UnB
collection Repositório Institucional da UnB
repository.name.fl_str_mv Repositório Institucional da UnB - Universidade de Brasília (UnB)
repository.mail.fl_str_mv repositorio@unb.br
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