Order-chaos-order and invariant manifolds in the bounded planar Earth–Moon system

Detalhes bibliográficos
Autor(a) principal: de Oliveira, Vitor M.
Data de Publicação: 2020
Outros Autores: Sousa-Silva, Priscilla A. [UNESP], Caldas, Iberê L.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1007/s10569-020-09989-x
http://hdl.handle.net/11449/205519
Resumo: In this work, we investigate the Earth–Moon system, as modeled by the planar circular restricted three-body problem, and relate its dynamical properties to the underlying structure associated with specific invariant manifolds. We consider a range of Jacobi constant values for which the neck around the Lagrangian point L1 is always open, but the orbits are bounded due to Hill stability. First, we show that the system displays three different dynamical scenarios in the neighborhood of the Moon: two mixed ones, with regular and chaotic orbits, and an almost entirely chaotic one in between. We then analyze the transitions between these scenarios using the monodromy matrix theory and determine that they are given by two specific types of bifurcations. After that, we illustrate how the phase space configurations, particularly the shapes of stability regions and stickiness, are intrinsically related to the hyperbolic invariant manifolds of the Lyapunov orbits around L1 and also to the ones of some particular unstable periodic orbits. Lastly, we define transit time in a manner that is useful to depict dynamical trapping and show that the traced geometrical structures are also connected to the transport properties of the system.
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spelling Order-chaos-order and invariant manifolds in the bounded planar Earth–Moon systemChaosInvariant manifoldsRestricted three-body problemIn this work, we investigate the Earth–Moon system, as modeled by the planar circular restricted three-body problem, and relate its dynamical properties to the underlying structure associated with specific invariant manifolds. We consider a range of Jacobi constant values for which the neck around the Lagrangian point L1 is always open, but the orbits are bounded due to Hill stability. First, we show that the system displays three different dynamical scenarios in the neighborhood of the Moon: two mixed ones, with regular and chaotic orbits, and an almost entirely chaotic one in between. We then analyze the transitions between these scenarios using the monodromy matrix theory and determine that they are given by two specific types of bifurcations. After that, we illustrate how the phase space configurations, particularly the shapes of stability regions and stickiness, are intrinsically related to the hyperbolic invariant manifolds of the Lyapunov orbits around L1 and also to the ones of some particular unstable periodic orbits. Lastly, we define transit time in a manner that is useful to depict dynamical trapping and show that the traced geometrical structures are also connected to the transport properties of the system.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Institute of Physics USP - University of São Paulo, Rua do Matão, 1371 - Edif. Basílio Jafet, Cidade UniversitáriaUNESP - São Paulo State University, Avenida Professora Isette Corrêa Fontão, 505, Jardim das FloresUNESP - São Paulo State University, Avenida Professora Isette Corrêa Fontão, 505, Jardim das FloresFAPESP: 2018/03211-6Universidade de São Paulo (USP)Universidade Estadual Paulista (Unesp)de Oliveira, Vitor M.Sousa-Silva, Priscilla A. [UNESP]Caldas, Iberê L.2021-06-25T10:16:46Z2021-06-25T10:16:46Z2020-12-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1007/s10569-020-09989-xCelestial Mechanics and Dynamical Astronomy, v. 132, n. 11-12, 2020.1572-94780923-2958http://hdl.handle.net/11449/20551910.1007/s10569-020-09989-x2-s2.0-85096572551Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengCelestial Mechanics and Dynamical Astronomyinfo:eu-repo/semantics/openAccess2021-10-23T14:48:14Zoai:repositorio.unesp.br:11449/205519Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T16:51:38.400941Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Order-chaos-order and invariant manifolds in the bounded planar Earth–Moon system
title Order-chaos-order and invariant manifolds in the bounded planar Earth–Moon system
spellingShingle Order-chaos-order and invariant manifolds in the bounded planar Earth–Moon system
de Oliveira, Vitor M.
Chaos
Invariant manifolds
Restricted three-body problem
title_short Order-chaos-order and invariant manifolds in the bounded planar Earth–Moon system
title_full Order-chaos-order and invariant manifolds in the bounded planar Earth–Moon system
title_fullStr Order-chaos-order and invariant manifolds in the bounded planar Earth–Moon system
title_full_unstemmed Order-chaos-order and invariant manifolds in the bounded planar Earth–Moon system
title_sort Order-chaos-order and invariant manifolds in the bounded planar Earth–Moon system
author de Oliveira, Vitor M.
author_facet de Oliveira, Vitor M.
Sousa-Silva, Priscilla A. [UNESP]
Caldas, Iberê L.
author_role author
author2 Sousa-Silva, Priscilla A. [UNESP]
Caldas, Iberê L.
author2_role author
author
dc.contributor.none.fl_str_mv Universidade de São Paulo (USP)
Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv de Oliveira, Vitor M.
Sousa-Silva, Priscilla A. [UNESP]
Caldas, Iberê L.
dc.subject.por.fl_str_mv Chaos
Invariant manifolds
Restricted three-body problem
topic Chaos
Invariant manifolds
Restricted three-body problem
description In this work, we investigate the Earth–Moon system, as modeled by the planar circular restricted three-body problem, and relate its dynamical properties to the underlying structure associated with specific invariant manifolds. We consider a range of Jacobi constant values for which the neck around the Lagrangian point L1 is always open, but the orbits are bounded due to Hill stability. First, we show that the system displays three different dynamical scenarios in the neighborhood of the Moon: two mixed ones, with regular and chaotic orbits, and an almost entirely chaotic one in between. We then analyze the transitions between these scenarios using the monodromy matrix theory and determine that they are given by two specific types of bifurcations. After that, we illustrate how the phase space configurations, particularly the shapes of stability regions and stickiness, are intrinsically related to the hyperbolic invariant manifolds of the Lyapunov orbits around L1 and also to the ones of some particular unstable periodic orbits. Lastly, we define transit time in a manner that is useful to depict dynamical trapping and show that the traced geometrical structures are also connected to the transport properties of the system.
publishDate 2020
dc.date.none.fl_str_mv 2020-12-01
2021-06-25T10:16:46Z
2021-06-25T10:16:46Z
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://dx.doi.org/10.1007/s10569-020-09989-x
Celestial Mechanics and Dynamical Astronomy, v. 132, n. 11-12, 2020.
1572-9478
0923-2958
http://hdl.handle.net/11449/205519
10.1007/s10569-020-09989-x
2-s2.0-85096572551
url http://dx.doi.org/10.1007/s10569-020-09989-x
http://hdl.handle.net/11449/205519
identifier_str_mv Celestial Mechanics and Dynamical Astronomy, v. 132, n. 11-12, 2020.
1572-9478
0923-2958
10.1007/s10569-020-09989-x
2-s2.0-85096572551
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Celestial Mechanics and Dynamical Astronomy
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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
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