Invariant manifolds near $L_{1}$ and $L_{2}$ in the Quasi-bicircular Problem

The quasi-bicircular problem (QBCP) is a periodic time-dependent perturbation of the Earth– Moon restricted three-body problem (RTBP) that accounts for the effect of the Sun. It is based on using a periodic solution of the Earth–Moon–Sun three-body problem to write the equations of motion of the inf...

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Autores: Rosales de Cáceres, José J., Jorba i Monte, Àngel, Jorba Cuscó, Marc
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/220610
Acceso en línea:https://hdl.handle.net/2445/220610
Access Level:acceso abierto
Palabra clave:Mecànica celeste
Problema dels n cossos
Varietats tòriques
Celestial mechanics
Many-body problem
Toric varieties
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spelling Invariant manifolds near $L_{1}$ and $L_{2}$ in the Quasi-bicircular ProblemRosales de Cáceres, José J.Jorba i Monte, ÀngelJorba Cuscó, MarcMecànica celesteProblema dels n cossosVarietats tòriquesCelestial mechanicsMany-body problemToric varietiesThe quasi-bicircular problem (QBCP) is a periodic time-dependent perturbation of the Earth– Moon restricted three-body problem (RTBP) that accounts for the effect of the Sun. It is based on using a periodic solution of the Earth–Moon–Sun three-body problem to write the equations of motion of the infinitesimal particle. The paper focuses on the dynamics near the $L_1$ and $L_2$ points of the Earth–Moon system in the QBCP. By means of a periodic time-dependent reduction to the center manifold, we show the existence of two families of quasi-periodic Lyapunov orbits around $L_1$ (resp. $L_2$) with two basic frequencies. The first of these two families is contained in the Earth–Moon plane and undergoes an out-of-plane (quasi-periodic) pitchfork bifurcation giving rise to a family of quasi-periodic Halo orbits. This analysis is complemented with the continuation of families of 2D tori. In particular, the planar and vertical Lyapunov families are continued, and their stability analyzed. Finally, examples of invariant manifolds associated with invariant 2D tori around the $L_2$ that pass close to the Earth are shown. This phenomenon is not observed in the RTBP and opens the room to direct transfers from the Earth to the Earth–Moon $L_2$ region.Springer Verlag2025202520232025info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersion47 p.application/pdfhttps://hdl.handle.net/2445/220610Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésReproducció del document publicat a: https://doi.org/10.1007/s10569-023-10129-4Celestial Mechanics and Dynamical Astronomy, 2023, vol. 135https://doi.org/10.1007/s10569-023-10129-4cc by (c) José J. Rosales de Cáceres et al., 2023http://creativecommons.org/licenses/by/3.0/es/info:eu-repo/semantics/openAccessoai:recercat.cat:2445/2206102026-05-29T05:05:01Z
dc.title.none.fl_str_mv Invariant manifolds near $L_{1}$ and $L_{2}$ in the Quasi-bicircular Problem
title Invariant manifolds near $L_{1}$ and $L_{2}$ in the Quasi-bicircular Problem
spellingShingle Invariant manifolds near $L_{1}$ and $L_{2}$ in the Quasi-bicircular Problem
Rosales de Cáceres, José J.
Mecànica celeste
Problema dels n cossos
Varietats tòriques
Celestial mechanics
Many-body problem
Toric varieties
title_short Invariant manifolds near $L_{1}$ and $L_{2}$ in the Quasi-bicircular Problem
title_full Invariant manifolds near $L_{1}$ and $L_{2}$ in the Quasi-bicircular Problem
title_fullStr Invariant manifolds near $L_{1}$ and $L_{2}$ in the Quasi-bicircular Problem
title_full_unstemmed Invariant manifolds near $L_{1}$ and $L_{2}$ in the Quasi-bicircular Problem
title_sort Invariant manifolds near $L_{1}$ and $L_{2}$ in the Quasi-bicircular Problem
dc.creator.none.fl_str_mv Rosales de Cáceres, José J.
Jorba i Monte, Àngel
Jorba Cuscó, Marc
author Rosales de Cáceres, José J.
author_facet Rosales de Cáceres, José J.
Jorba i Monte, Àngel
Jorba Cuscó, Marc
author_role author
author2 Jorba i Monte, Àngel
Jorba Cuscó, Marc
author2_role author
author
dc.subject.none.fl_str_mv Mecànica celeste
Problema dels n cossos
Varietats tòriques
Celestial mechanics
Many-body problem
Toric varieties
topic Mecànica celeste
Problema dels n cossos
Varietats tòriques
Celestial mechanics
Many-body problem
Toric varieties
description The quasi-bicircular problem (QBCP) is a periodic time-dependent perturbation of the Earth– Moon restricted three-body problem (RTBP) that accounts for the effect of the Sun. It is based on using a periodic solution of the Earth–Moon–Sun three-body problem to write the equations of motion of the infinitesimal particle. The paper focuses on the dynamics near the $L_1$ and $L_2$ points of the Earth–Moon system in the QBCP. By means of a periodic time-dependent reduction to the center manifold, we show the existence of two families of quasi-periodic Lyapunov orbits around $L_1$ (resp. $L_2$) with two basic frequencies. The first of these two families is contained in the Earth–Moon plane and undergoes an out-of-plane (quasi-periodic) pitchfork bifurcation giving rise to a family of quasi-periodic Halo orbits. This analysis is complemented with the continuation of families of 2D tori. In particular, the planar and vertical Lyapunov families are continued, and their stability analyzed. Finally, examples of invariant manifolds associated with invariant 2D tori around the $L_2$ that pass close to the Earth are shown. This phenomenon is not observed in the RTBP and opens the room to direct transfers from the Earth to the Earth–Moon $L_2$ region.
publishDate 2023
dc.date.none.fl_str_mv 2023
2025
2025
2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/220610
url https://hdl.handle.net/2445/220610
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Reproducció del document publicat a: https://doi.org/10.1007/s10569-023-10129-4
Celestial Mechanics and Dynamical Astronomy, 2023, vol. 135
https://doi.org/10.1007/s10569-023-10129-4
dc.rights.none.fl_str_mv cc by (c) José J. Rosales de Cáceres et al., 2023
http://creativecommons.org/licenses/by/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc by (c) José J. Rosales de Cáceres et al., 2023
http://creativecommons.org/licenses/by/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 47 p.
application/pdf
dc.publisher.none.fl_str_mv Springer Verlag
publisher.none.fl_str_mv Springer Verlag
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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