Problems of maximal mean resistance on the plane

Detalhes bibliográficos
Autor(a) principal: Plakhov, Alexander
Data de Publicação: 2007
Outros Autores: Gouveia, Paulo D.F.
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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spelling 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
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dc.publisher.none.fl_str_mv IOP
publisher.none.fl_str_mv IOP
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