The divergence and curl in arbitrary basis
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| Tác giả chính: | |
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| Ngày xuất bản: | 2019 |
| Tác giả khác: | , , |
| Định dạng: | Article |
| Ngôn ngữ: | eng |
| Nguồn: | Repositório Institucional da UnB |
| Download full: | https://repositorio.unb.br/handle/10482/36550 https://doi.org/10.1590/1806-9126-rbef-2018-0082 http://orcid.org/0000-0003-4650-5947 |
Tóm tắt: | 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. |
| _version_ | 1871442641154998272 |
|---|---|
| author | Medeiros, Waleska Priscylla Florencio de |
| author2 | Lima, Rodrigo Ramos de Andrade, Vanessa Carvalho de Müller, Daniel |
| author2_role | author author author |
| author_browse | Andrade, Vanessa Carvalho de Lima, Rodrigo Ramos de Medeiros, Waleska Priscylla Florencio de Müller, Daniel |
| author_facet | Medeiros, Waleska Priscylla Florencio de Lima, Rodrigo Ramos de Andrade, Vanessa Carvalho de Müller, Daniel |
| author_role | author |
| bitstream.checksum.fl_str_mv | 99da08b53f493c6cd32c75dd658636a1 |
| bitstream.checksumAlgorithm.fl_str_mv | MD5 |
| bitstream.url.fl_str_mv | http://repositorio2.unb.br/jspui/bitstream/10482/36550/1/ARTIGO_DivergenceCurlArbitrary.pdf |
| collection | Repositório Institucional da UnB |
| dc.contributor.author.fl_str_mv | Medeiros, Waleska Priscylla Florencio de Lima, Rodrigo Ramos de Andrade, Vanessa Carvalho de Müller, Daniel |
| dc.date.accessioned.fl_str_mv | 2020-01-24T10:31:46Z |
| dc.date.available.fl_str_mv | 2020-01-24T10:31:46Z |
| dc.date.issued.fl_str_mv | 2019 |
| dc.identifier.citation.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. |
| dc.identifier.doi.pt_BR.fl_str_mv | https://doi.org/10.1590/1806-9126-rbef-2018-0082 |
| dc.identifier.orcid.none.fl_str_mv | http://orcid.org/0000-0003-4650-5947 |
| dc.identifier.uri.fl_str_mv | https://repositorio.unb.br/handle/10482/36550 |
| dc.language.iso.fl_str_mv | eng |
| dc.publisher.none.fl_str_mv | Sociedade Brasileira de Física |
| dc.rights.driver.fl_str_mv | (CC BY) - Licença Creative Commons info:eu-repo/semantics/openAccess |
| dc.source.none.fl_str_mv | reponame:Repositório Institucional da UnB instname:Universidade de Brasília (UnB) instacron:UNB |
| dc.subject.keyword.none.fl_str_mv | Geometria diferencial |
| dc.subject.keyword.pt_BR.fl_str_mv | Cálculo vetorial |
| dc.title.pt_BR.fl_str_mv | The divergence and curl in arbitrary basis |
| dc.type.driver.fl_str_mv | info:eu-repo/semantics/article |
| dc.type.status.fl_str_mv | info:eu-repo/semantics/publishedVersion |
| 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. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | UNB_fa187f7ba500197ceeca67fe64941d5c |
| 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. |
| instacron_str | UNB |
| institution | UNB |
| instname_str | Universidade de Brasília (UnB) |
| language | eng |
| network_acronym_str | UNB |
| network_name_str | Repositório Institucional da UnB |
| oai_identifier_str | oai:repositorio.unb.br:10482/36550 |
| publishDate | 2019 |
| publishDateSort | 2019 |
| publisher.none.fl_str_mv | Sociedade Brasileira de Física |
| reponame_str | Repositório Institucional da UnB |
| repository.mail.fl_str_mv | repositorio@unb.br |
| repository.name.fl_str_mv | Repositório Institucional da UnB - Universidade de Brasília (UnB) |
| repository_id_str | |
| rights_invalid_str_mv | (CC BY) - Licença Creative Commons |
| spelling | Medeiros, Waleska Priscylla Florencio deLima, Rodrigo Ramos deAndrade, Vanessa Carvalho deMüller, Daniel2020-01-24T10:31:46Z2020-01-24T10:31:46Z2019MEDEIROS, 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/0000-0003-4650-5947Sociedade Brasileira de Física(CC BY) - Licença Creative Commonsinfo:eu-repo/semantics/openAccessThe divergence and curl in arbitrary basisinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleCálculo 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.engreponame:Repositório Institucional da UnBinstname:Universidade de Brasília (UnB)instacron:UNBORIGINALARTIGO_DivergenceCurlArbitrary.pdfapplication/pdf3519541http://repositorio2.unb.br/jspui/bitstream/10482/36550/1/ARTIGO_DivergenceCurlArbitrary.pdf99da08b53f493c6cd32c75dd658636a1MD51open access10482/365502023-05-26 21:19:55.379open accessoai: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) |
| spellingShingle | The divergence and curl in arbitrary basis Medeiros, Waleska Priscylla Florencio de Cálculo vetorial Geometria diferencial |
| status_str | publishedVersion |
| title | 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_short | The divergence and curl in arbitrary basis |
| title_sort | The divergence and curl in arbitrary basis |
| topic | Cálculo vetorial Geometria diferencial |
| 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 |