Motion in rotating Earth: exact solutions and second-order effects of noninertial forces

Detalhes bibliográficos
Autor(a) principal: Diniz,Eduardo Moraes
Data de Publicação: 2022
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Revista Brasileira de Ensino de Física (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172022000100418
Resumo: The motion of a particle evaluated from the noninertial frame of the rotating Earth with constant angular velocity ω is solved analytically without carrying out a priori approximations, that is, considering both the Coriolis and the centrifugal terms. Position vector solutions written in terms of generic initial conditions were obtained from a decoupled sixth-order equation of motion, obtained using a fully vectorial approach, without specifically resorting to coordinates. By comparing the exact solutions for the complete and approximate (ignoring the centrifugal term from the beginning) problems, great differences can be seen in the order of the decoupled differential equation as well as in the temporal dependencies of the noninertial terms of the solutions. Noninertial effects for the solution were classified according to the order of magnitude in ω, where first-order effects are oriented east-west and the second-order ones are oriented north-south.
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spelling Motion in rotating Earth: exact solutions and second-order effects of noninertial forcesNoninertial framesNoninertial effectsSecond-order effectsMotion in rotating EarthThe motion of a particle evaluated from the noninertial frame of the rotating Earth with constant angular velocity ω is solved analytically without carrying out a priori approximations, that is, considering both the Coriolis and the centrifugal terms. Position vector solutions written in terms of generic initial conditions were obtained from a decoupled sixth-order equation of motion, obtained using a fully vectorial approach, without specifically resorting to coordinates. By comparing the exact solutions for the complete and approximate (ignoring the centrifugal term from the beginning) problems, great differences can be seen in the order of the decoupled differential equation as well as in the temporal dependencies of the noninertial terms of the solutions. Noninertial effects for the solution were classified according to the order of magnitude in ω, where first-order effects are oriented east-west and the second-order ones are oriented north-south.Sociedade Brasileira de Física2022-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172022000100418Revista Brasileira de Ensino de Física v.44 2022reponame:Revista Brasileira de Ensino de Física (Online)instname:Sociedade Brasileira de Física (SBF)instacron:SBF10.1590/1806-9126-rbef-2021-0369info:eu-repo/semantics/openAccessDiniz,Eduardo Moraeseng2022-02-08T00:00:00Zoai:scielo:S1806-11172022000100418Revistahttp://www.sbfisica.org.br/rbef/https://old.scielo.br/oai/scielo-oai.php||marcio@sbfisica.org.br1806-91261806-1117opendoar:2022-02-08T00:00Revista Brasileira de Ensino de Física (Online) - Sociedade Brasileira de Física (SBF)false
dc.title.none.fl_str_mv Motion in rotating Earth: exact solutions and second-order effects of noninertial forces
title Motion in rotating Earth: exact solutions and second-order effects of noninertial forces
spellingShingle Motion in rotating Earth: exact solutions and second-order effects of noninertial forces
Diniz,Eduardo Moraes
Noninertial frames
Noninertial effects
Second-order effects
Motion in rotating Earth
title_short Motion in rotating Earth: exact solutions and second-order effects of noninertial forces
title_full Motion in rotating Earth: exact solutions and second-order effects of noninertial forces
title_fullStr Motion in rotating Earth: exact solutions and second-order effects of noninertial forces
title_full_unstemmed Motion in rotating Earth: exact solutions and second-order effects of noninertial forces
title_sort Motion in rotating Earth: exact solutions and second-order effects of noninertial forces
author Diniz,Eduardo Moraes
author_facet Diniz,Eduardo Moraes
author_role author
dc.contributor.author.fl_str_mv Diniz,Eduardo Moraes
dc.subject.por.fl_str_mv Noninertial frames
Noninertial effects
Second-order effects
Motion in rotating Earth
topic Noninertial frames
Noninertial effects
Second-order effects
Motion in rotating Earth
description The motion of a particle evaluated from the noninertial frame of the rotating Earth with constant angular velocity ω is solved analytically without carrying out a priori approximations, that is, considering both the Coriolis and the centrifugal terms. Position vector solutions written in terms of generic initial conditions were obtained from a decoupled sixth-order equation of motion, obtained using a fully vectorial approach, without specifically resorting to coordinates. By comparing the exact solutions for the complete and approximate (ignoring the centrifugal term from the beginning) problems, great differences can be seen in the order of the decoupled differential equation as well as in the temporal dependencies of the noninertial terms of the solutions. Noninertial effects for the solution were classified according to the order of magnitude in ω, where first-order effects are oriented east-west and the second-order ones are oriented north-south.
publishDate 2022
dc.date.none.fl_str_mv 2022-01-01
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=S1806-11172022000100418
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172022000100418
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/1806-9126-rbef-2021-0369
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 Sociedade Brasileira de Física
publisher.none.fl_str_mv Sociedade Brasileira de Física
dc.source.none.fl_str_mv Revista Brasileira de Ensino de Física v.44 2022
reponame:Revista Brasileira de Ensino de Física (Online)
instname:Sociedade Brasileira de Física (SBF)
instacron:SBF
instname_str Sociedade Brasileira de Física (SBF)
instacron_str SBF
institution SBF
reponame_str Revista Brasileira de Ensino de Física (Online)
collection Revista Brasileira de Ensino de Física (Online)
repository.name.fl_str_mv Revista Brasileira de Ensino de Física (Online) - Sociedade Brasileira de Física (SBF)
repository.mail.fl_str_mv ||marcio@sbfisica.org.br
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