Billiard in a rotating half-plane

Detalhes bibliográficos
Autor(a) principal: Kryzhevich, Sergey
Data de Publicação: 2023
Outros Autores: Plakhov, Alexander
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Texto Completo: http://hdl.handle.net/10773/39997
Resumo: The main objective of this research is to study the properties of a billiard system in an unbounded domain with moving boundary. We consider a system consisting of an infinite rod (a straight line) and a ball (a massless point) on the plane. The rod rotates uniformly around one of its points and experiences elastic collisions with the ball. We define a mathematical model for the dynamics of such a system and write down asymptotic formulae for its motions. In particular, we determine existence and uniqueness of solutions. We find all possible grazing impacts of the ball. Besides, we demonstrate that for almost every initial condition, the ball goes to infinity exponentially fast, with the time intervals between neighboring collisions tending to zero. The approach developed in this paper is an original combination of methods of Billiards and Vibro-Impact Dynamics. It could be a base for studying more complicated systems of similar types.
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spelling Billiard in a rotating half-planeBilliardsMoving boundaryElastic impactSlidingThe main objective of this research is to study the properties of a billiard system in an unbounded domain with moving boundary. We consider a system consisting of an infinite rod (a straight line) and a ball (a massless point) on the plane. The rod rotates uniformly around one of its points and experiences elastic collisions with the ball. We define a mathematical model for the dynamics of such a system and write down asymptotic formulae for its motions. In particular, we determine existence and uniqueness of solutions. We find all possible grazing impacts of the ball. Besides, we demonstrate that for almost every initial condition, the ball goes to infinity exponentially fast, with the time intervals between neighboring collisions tending to zero. The approach developed in this paper is an original combination of methods of Billiards and Vibro-Impact Dynamics. It could be a base for studying more complicated systems of similar types.Springer2024-01-08T16:01:14Z2023-07-03T00:00:00Z2023-07-03info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/39997eng1079-272410.1007/s10883-023-09655-zKryzhevich, SergeyPlakhov, Alexanderinfo:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-05-06T04:28:45Zoai:ria.ua.pt:10773/39997Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T14:09:58.932016Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv Billiard in a rotating half-plane
title Billiard in a rotating half-plane
spellingShingle Billiard in a rotating half-plane
Kryzhevich, Sergey
Billiards
Moving boundary
Elastic impact
Sliding
title_short Billiard in a rotating half-plane
title_full Billiard in a rotating half-plane
title_fullStr Billiard in a rotating half-plane
title_full_unstemmed Billiard in a rotating half-plane
title_sort Billiard in a rotating half-plane
author Kryzhevich, Sergey
author_facet Kryzhevich, Sergey
Plakhov, Alexander
author_role author
author2 Plakhov, Alexander
author2_role author
dc.contributor.author.fl_str_mv Kryzhevich, Sergey
Plakhov, Alexander
dc.subject.por.fl_str_mv Billiards
Moving boundary
Elastic impact
Sliding
topic Billiards
Moving boundary
Elastic impact
Sliding
description The main objective of this research is to study the properties of a billiard system in an unbounded domain with moving boundary. We consider a system consisting of an infinite rod (a straight line) and a ball (a massless point) on the plane. The rod rotates uniformly around one of its points and experiences elastic collisions with the ball. We define a mathematical model for the dynamics of such a system and write down asymptotic formulae for its motions. In particular, we determine existence and uniqueness of solutions. We find all possible grazing impacts of the ball. Besides, we demonstrate that for almost every initial condition, the ball goes to infinity exponentially fast, with the time intervals between neighboring collisions tending to zero. The approach developed in this paper is an original combination of methods of Billiards and Vibro-Impact Dynamics. It could be a base for studying more complicated systems of similar types.
publishDate 2023
dc.date.none.fl_str_mv 2023-07-03T00:00:00Z
2023-07-03
2024-01-08T16:01:14Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/39997
url http://hdl.handle.net/10773/39997
dc.language.iso.fl_str_mv eng
language eng
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10.1007/s10883-023-09655-z
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
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dc.format.none.fl_str_mv application/pdf
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instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
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