Dissipative gravitational bouncer on a vibrating surface
Autor(a) principal: | |
---|---|
Data de Publicação: | 2017 |
Outros Autores: | |
Tipo de documento: | Artigo de conferência |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1088/1742-6596/936/1/012003 http://hdl.handle.net/11449/175804 |
Resumo: | We study the dynamical behavior of a particle flying under the influence of a gravitational field, with dissipation constant λ (Stokes-like), colliding successive times against a rigid surface vibrating harmonically with restitution coefficient α. We define re-scaled dimensionless dynamical variables, such as the relative particle velocity Ω with respect to the surface's velocity; and the real parameter τ accounting for the temporal evolution of the system. At the particle-surface contact point and for the k′th collision, we construct the mapping described by (τk ; Ωk ) in order to analyze the system's nonlinear dynamical behavior. From the dynamical mapping, the fixed point trajectory is computed and its stability is analyzed. We find the dynamical behavior of the fixed point trajectory to be stable or unstable, depending on the values of the re-scaled vibrating surface amplitude Γ, the restitution coefficient α and the damping constant λ. Other important dynamical aspects such as the phase space volume and the one cycle vibrating surface (decomposed into absorbing and transmitting regions) are also discussed. Furthermore, the model rescues well known results in the limit λ = 0. |
id |
UNSP_fc06dfd53d95bd7886dc61ee3e6dfa5c |
---|---|
oai_identifier_str |
oai:repositorio.unesp.br:11449/175804 |
network_acronym_str |
UNSP |
network_name_str |
Repositório Institucional da UNESP |
repository_id_str |
2946 |
spelling |
Dissipative gravitational bouncer on a vibrating surfaceWe study the dynamical behavior of a particle flying under the influence of a gravitational field, with dissipation constant λ (Stokes-like), colliding successive times against a rigid surface vibrating harmonically with restitution coefficient α. We define re-scaled dimensionless dynamical variables, such as the relative particle velocity Ω with respect to the surface's velocity; and the real parameter τ accounting for the temporal evolution of the system. At the particle-surface contact point and for the k′th collision, we construct the mapping described by (τk ; Ωk ) in order to analyze the system's nonlinear dynamical behavior. From the dynamical mapping, the fixed point trajectory is computed and its stability is analyzed. We find the dynamical behavior of the fixed point trajectory to be stable or unstable, depending on the values of the re-scaled vibrating surface amplitude Γ, the restitution coefficient α and the damping constant λ. Other important dynamical aspects such as the phase space volume and the one cycle vibrating surface (decomposed into absorbing and transmitting regions) are also discussed. Furthermore, the model rescues well known results in the limit λ = 0.Fundação de Amparo à Pesquisa do Estado de GoiásDepartamento de Física UAEF Universidade Federal de GoiásDepartamento de Física IGCE UNESPDepartamento de Física IGCE UNESPUniversidade Federal de Goiás (UFG)Universidade Estadual Paulista (Unesp)Espinoza Ortiz, J. S.Lagos, R. E. [UNESP]2018-12-11T17:17:35Z2018-12-11T17:17:35Z2017-12-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/conferenceObjectapplication/pdfhttp://dx.doi.org/10.1088/1742-6596/936/1/012003Journal of Physics: Conference Series, v. 936, n. 1, 2017.1742-65961742-6588http://hdl.handle.net/11449/17580410.1088/1742-6596/936/1/0120032-s2.0-850412339892-s2.0-85041233989.pdfScopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal of Physics: Conference Series0,2410,241info:eu-repo/semantics/openAccess2023-10-02T06:00:53Zoai:repositorio.unesp.br:11449/175804Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T13:42:02.382331Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Dissipative gravitational bouncer on a vibrating surface |
title |
Dissipative gravitational bouncer on a vibrating surface |
spellingShingle |
Dissipative gravitational bouncer on a vibrating surface Espinoza Ortiz, J. S. |
title_short |
Dissipative gravitational bouncer on a vibrating surface |
title_full |
Dissipative gravitational bouncer on a vibrating surface |
title_fullStr |
Dissipative gravitational bouncer on a vibrating surface |
title_full_unstemmed |
Dissipative gravitational bouncer on a vibrating surface |
title_sort |
Dissipative gravitational bouncer on a vibrating surface |
author |
Espinoza Ortiz, J. S. |
author_facet |
Espinoza Ortiz, J. S. Lagos, R. E. [UNESP] |
author_role |
author |
author2 |
Lagos, R. E. [UNESP] |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Federal de Goiás (UFG) Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Espinoza Ortiz, J. S. Lagos, R. E. [UNESP] |
description |
We study the dynamical behavior of a particle flying under the influence of a gravitational field, with dissipation constant λ (Stokes-like), colliding successive times against a rigid surface vibrating harmonically with restitution coefficient α. We define re-scaled dimensionless dynamical variables, such as the relative particle velocity Ω with respect to the surface's velocity; and the real parameter τ accounting for the temporal evolution of the system. At the particle-surface contact point and for the k′th collision, we construct the mapping described by (τk ; Ωk ) in order to analyze the system's nonlinear dynamical behavior. From the dynamical mapping, the fixed point trajectory is computed and its stability is analyzed. We find the dynamical behavior of the fixed point trajectory to be stable or unstable, depending on the values of the re-scaled vibrating surface amplitude Γ, the restitution coefficient α and the damping constant λ. Other important dynamical aspects such as the phase space volume and the one cycle vibrating surface (decomposed into absorbing and transmitting regions) are also discussed. Furthermore, the model rescues well known results in the limit λ = 0. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017-12-01 2018-12-11T17:17:35Z 2018-12-11T17:17:35Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/conferenceObject |
format |
conferenceObject |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1088/1742-6596/936/1/012003 Journal of Physics: Conference Series, v. 936, n. 1, 2017. 1742-6596 1742-6588 http://hdl.handle.net/11449/175804 10.1088/1742-6596/936/1/012003 2-s2.0-85041233989 2-s2.0-85041233989.pdf |
url |
http://dx.doi.org/10.1088/1742-6596/936/1/012003 http://hdl.handle.net/11449/175804 |
identifier_str_mv |
Journal of Physics: Conference Series, v. 936, n. 1, 2017. 1742-6596 1742-6588 10.1088/1742-6596/936/1/012003 2-s2.0-85041233989 2-s2.0-85041233989.pdf |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Journal of Physics: Conference Series 0,241 0,241 |
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.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808128267848253440 |