Re-Evaluating the Classical Falling Body Problem
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Outros Autores: | , , , |
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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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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