Order-chaos-order and invariant manifolds in the bounded planar Earth–Moon system
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Outros Autores: | , |
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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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 |
|
_version_ |
1808128711037288448 |