Problems of maximal mean resistance on the plane
Autor(a) principal: | |
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Data de Publicação: | 2007 |
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/10198/1647 |
Resumo: | A two-dimensional body moves through a rarefied medium; the collisions of the medium particles with the body are absolutely elastic.The body performs both translational and slow rotational motion. It is required to select the body, from a given class of bodies, such that the average force of resistance of the medium to its motion is maximal. There are presented numerical and analytical results concerning this problem. In particular, the maximum resistance in the class of bodies contained in a convex body K is proved to be 1.5 times resistance of K. The maximum is attained on a sequence of bodies with very complicated boundary. The numerical study was made for somewhat more restricted classes of bodies. The obtained values of resistance are slightly lower, but the boundary of obtained bodies is much simpler, as compared to the analytical solutions. |
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Problems of maximal mean resistance on the planeBodies of maximal resistanceShape optimizationBilliardsNumerical simulationNewton-like aerodynamic problemA two-dimensional body moves through a rarefied medium; the collisions of the medium particles with the body are absolutely elastic.The body performs both translational and slow rotational motion. It is required to select the body, from a given class of bodies, such that the average force of resistance of the medium to its motion is maximal. There are presented numerical and analytical results concerning this problem. In particular, the maximum resistance in the class of bodies contained in a convex body K is proved to be 1.5 times resistance of K. The maximum is attained on a sequence of bodies with very complicated boundary. The numerical study was made for somewhat more restricted classes of bodies. The obtained values of resistance are slightly lower, but the boundary of obtained bodies is much simpler, as compared to the analytical solutions.This work was supported by Centre for Research on Optimization and Control (CEOC) from the ”Fundação para a Ciência e a Tecnologia ” (FCT), cofinanced by the European Community Fund FEDER/POCTI.IOPBiblioteca Digital do IPBPlakhov, AlexanderGouveia, Paulo D.F.2010-02-01T21:39:47Z20072007-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10198/1647engPlakhov, Alexander; Gouveia, Paulo D.F. (2007). Problems of maximal mean resistance on the plane. Nonlinearity. ISSN 1361-6544. 20:9, p. 2271-22871361-654410.1088/0951-7715/20/9/013info: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:RCAAP2023-11-21T10:05:39Zoai:bibliotecadigital.ipb.pt:10198/1647Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:55:06.262423Repositório 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 |
Problems of maximal mean resistance on the plane |
title |
Problems of maximal mean resistance on the plane |
spellingShingle |
Problems of maximal mean resistance on the plane Plakhov, Alexander Bodies of maximal resistance Shape optimization Billiards Numerical simulation Newton-like aerodynamic problem |
title_short |
Problems of maximal mean resistance on the plane |
title_full |
Problems of maximal mean resistance on the plane |
title_fullStr |
Problems of maximal mean resistance on the plane |
title_full_unstemmed |
Problems of maximal mean resistance on the plane |
title_sort |
Problems of maximal mean resistance on the plane |
author |
Plakhov, Alexander |
author_facet |
Plakhov, Alexander Gouveia, Paulo D.F. |
author_role |
author |
author2 |
Gouveia, Paulo D.F. |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Biblioteca Digital do IPB |
dc.contributor.author.fl_str_mv |
Plakhov, Alexander Gouveia, Paulo D.F. |
dc.subject.por.fl_str_mv |
Bodies of maximal resistance Shape optimization Billiards Numerical simulation Newton-like aerodynamic problem |
topic |
Bodies of maximal resistance Shape optimization Billiards Numerical simulation Newton-like aerodynamic problem |
description |
A two-dimensional body moves through a rarefied medium; the collisions of the medium particles with the body are absolutely elastic.The body performs both translational and slow rotational motion. It is required to select the body, from a given class of bodies, such that the average force of resistance of the medium to its motion is maximal. There are presented numerical and analytical results concerning this problem. In particular, the maximum resistance in the class of bodies contained in a convex body K is proved to be 1.5 times resistance of K. The maximum is attained on a sequence of bodies with very complicated boundary. The numerical study was made for somewhat more restricted classes of bodies. The obtained values of resistance are slightly lower, but the boundary of obtained bodies is much simpler, as compared to the analytical solutions. |
publishDate |
2007 |
dc.date.none.fl_str_mv |
2007 2007-01-01T00:00:00Z 2010-02-01T21:39:47Z |
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/10198/1647 |
url |
http://hdl.handle.net/10198/1647 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Plakhov, Alexander; Gouveia, Paulo D.F. (2007). Problems of maximal mean resistance on the plane. Nonlinearity. ISSN 1361-6544. 20:9, p. 2271-2287 1361-6544 10.1088/0951-7715/20/9/013 |
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 |
IOP |
publisher.none.fl_str_mv |
IOP |
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) |
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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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1799135152901718016 |