A direct approach to area change in continuum mechanics

Detalhes bibliográficos
Autor(a) principal: Martins,L. C.
Data de Publicação: 2003
Outros Autores: Oliveira,R. F. de
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Journal of the Brazilian Society of Mechanical Sciences and Engineering (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1678-58782003000300015
Resumo: In this note we use elementary facts from 3-dimensional linear algebra to demonstrate the formula for area changes under arbitrary linear maps A : R³ -> R³. We do it in general, from a hint given by the well known invertible case, which is an important result used in continuum mechanics. An intrinsic formula for the case when rank A = 2 is obtained and we finish by showing that we are really exploring a property of the cofactor matrix of A for an orthonormal basis.
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spelling A direct approach to area change in continuum mechanicsCofactor matrixlinear algebraIn this note we use elementary facts from 3-dimensional linear algebra to demonstrate the formula for area changes under arbitrary linear maps A : R³ -> R³. We do it in general, from a hint given by the well known invertible case, which is an important result used in continuum mechanics. An intrinsic formula for the case when rank A = 2 is obtained and we finish by showing that we are really exploring a property of the cofactor matrix of A for an orthonormal basis.Associação Brasileira de Engenharia e Ciências Mecânicas - ABCM2003-09-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1678-58782003000300015Journal of the Brazilian Society of Mechanical Sciences and Engineering v.25 n.3 2003reponame:Journal of the Brazilian Society of Mechanical Sciences and Engineering (Online)instname:Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)instacron:ABCM10.1590/S1678-58782003000300015info:eu-repo/semantics/openAccessMartins,L. C.Oliveira,R. F. deeng2004-03-18T00:00:00Zoai:scielo:S1678-58782003000300015Revistahttps://www.scielo.br/j/jbsmse/https://old.scielo.br/oai/scielo-oai.php||abcm@abcm.org.br1806-36911678-5878opendoar:2004-03-18T00:00Journal of the Brazilian Society of Mechanical Sciences and Engineering (Online) - Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)false
dc.title.none.fl_str_mv A direct approach to area change in continuum mechanics
title A direct approach to area change in continuum mechanics
spellingShingle A direct approach to area change in continuum mechanics
Martins,L. C.
Cofactor matrix
linear algebra
title_short A direct approach to area change in continuum mechanics
title_full A direct approach to area change in continuum mechanics
title_fullStr A direct approach to area change in continuum mechanics
title_full_unstemmed A direct approach to area change in continuum mechanics
title_sort A direct approach to area change in continuum mechanics
author Martins,L. C.
author_facet Martins,L. C.
Oliveira,R. F. de
author_role author
author2 Oliveira,R. F. de
author2_role author
dc.contributor.author.fl_str_mv Martins,L. C.
Oliveira,R. F. de
dc.subject.por.fl_str_mv Cofactor matrix
linear algebra
topic Cofactor matrix
linear algebra
description In this note we use elementary facts from 3-dimensional linear algebra to demonstrate the formula for area changes under arbitrary linear maps A : R³ -> R³. We do it in general, from a hint given by the well known invertible case, which is an important result used in continuum mechanics. An intrinsic formula for the case when rank A = 2 is obtained and we finish by showing that we are really exploring a property of the cofactor matrix of A for an orthonormal basis.
publishDate 2003
dc.date.none.fl_str_mv 2003-09-01
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=S1678-58782003000300015
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1678-58782003000300015
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S1678-58782003000300015
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 Associação Brasileira de Engenharia e Ciências Mecânicas - ABCM
publisher.none.fl_str_mv Associação Brasileira de Engenharia e Ciências Mecânicas - ABCM
dc.source.none.fl_str_mv Journal of the Brazilian Society of Mechanical Sciences and Engineering v.25 n.3 2003
reponame:Journal of the Brazilian Society of Mechanical Sciences and Engineering (Online)
instname:Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)
instacron:ABCM
instname_str Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)
instacron_str ABCM
institution ABCM
reponame_str Journal of the Brazilian Society of Mechanical Sciences and Engineering (Online)
collection Journal of the Brazilian Society of Mechanical Sciences and Engineering (Online)
repository.name.fl_str_mv Journal of the Brazilian Society of Mechanical Sciences and Engineering (Online) - Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)
repository.mail.fl_str_mv ||abcm@abcm.org.br
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