Re-Evaluating the Classical Falling Body Problem

Detalhes bibliográficos
Autor(a) principal: El-Zahar, Essam R.
Data de Publicação: 2020
Outros Autores: Ebaid, Abdelhalim, Aljohani, Abdulrahman F., Machado, J. A. Tenreiro, Baleanu, Dumitru
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.22/19451
Resumo: This paper re-analyzes the falling body problem in three dimensions, taking into account the effect of the Earth’s rotation (ER). Accordingly, the analytic solution of the three-dimensional model is obtained. Since the ER is quite slow, the three coupled differential equations of motion are usually approximated by neglecting all high order terms. Furthermore, the theoretical aspects describing the nature of the falling point in the rotating frame and the original inertial frame are proved. The theoretical and numerical results are illustrated and discussed.
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spelling Re-Evaluating the Classical Falling Body ProblemFalling body problemAngular velocityProjectile motionThree dimensionsEarth’s rotationThis paper re-analyzes the falling body problem in three dimensions, taking into account the effect of the Earth’s rotation (ER). Accordingly, the analytic solution of the three-dimensional model is obtained. Since the ER is quite slow, the three coupled differential equations of motion are usually approximated by neglecting all high order terms. Furthermore, the theoretical aspects describing the nature of the falling point in the rotating frame and the original inertial frame are proved. The theoretical and numerical results are illustrated and discussed.The authors would like to thank the referees for their valuable comments and suggestions, which helped to improve the manuscript. Moreover, the first author thanks Prince Sattam bin Abdulaziz University and Deanship of Scientific Research at Prince Sattam bin Abdulaziz University for their continuous support and encouragement.MDPIRepositório Científico do Instituto Politécnico do PortoEl-Zahar, Essam R.Ebaid, AbdelhalimAljohani, Abdulrahman F.Machado, J. A. TenreiroBaleanu, Dumitru2022-01-13T13:50:51Z20202020-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.22/19451eng10.3390/math8040553info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-03-13T13:13:23Zoai:recipp.ipp.pt:10400.22/19451Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:39:21.045515Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Re-Evaluating the Classical Falling Body Problem
title Re-Evaluating the Classical Falling Body Problem
spellingShingle Re-Evaluating the Classical Falling Body Problem
El-Zahar, Essam R.
Falling body problem
Angular velocity
Projectile motion
Three dimensions
Earth’s rotation
title_short Re-Evaluating the Classical Falling Body Problem
title_full Re-Evaluating the Classical Falling Body Problem
title_fullStr Re-Evaluating the Classical Falling Body Problem
title_full_unstemmed Re-Evaluating the Classical Falling Body Problem
title_sort Re-Evaluating the Classical Falling Body Problem
author El-Zahar, Essam R.
author_facet El-Zahar, Essam R.
Ebaid, Abdelhalim
Aljohani, Abdulrahman F.
Machado, J. A. Tenreiro
Baleanu, Dumitru
author_role author
author2 Ebaid, Abdelhalim
Aljohani, Abdulrahman F.
Machado, J. A. Tenreiro
Baleanu, Dumitru
author2_role author
author
author
author
dc.contributor.none.fl_str_mv Repositório Científico do Instituto Politécnico do Porto
dc.contributor.author.fl_str_mv El-Zahar, Essam R.
Ebaid, Abdelhalim
Aljohani, Abdulrahman F.
Machado, J. A. Tenreiro
Baleanu, Dumitru
dc.subject.por.fl_str_mv Falling body problem
Angular velocity
Projectile motion
Three dimensions
Earth’s rotation
topic Falling body problem
Angular velocity
Projectile motion
Three dimensions
Earth’s rotation
description This paper re-analyzes the falling body problem in three dimensions, taking into account the effect of the Earth’s rotation (ER). Accordingly, the analytic solution of the three-dimensional model is obtained. Since the ER is quite slow, the three coupled differential equations of motion are usually approximated by neglecting all high order terms. Furthermore, the theoretical aspects describing the nature of the falling point in the rotating frame and the original inertial frame are proved. The theoretical and numerical results are illustrated and discussed.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-01-01T00:00:00Z
2022-01-13T13:50:51Z
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/10400.22/19451
url http://hdl.handle.net/10400.22/19451
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.3390/math8040553
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv MDPI
publisher.none.fl_str_mv MDPI
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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