Simple tools to study global dynamics in non-axisymmetric galactic potentials - I

Autores
Cincotta, Pablo Miguel; Simó, C.
Año de publicación
2000
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In a first part we discuss the well-known problem of the motion of a star in a general non-axisymmetric 2D galactic potential by means of a very simple but almost universal system: the pendulum model. It is shown that both loop and box families of orbits arise as a natural consequence of the dynamics of the pendulum. An approximate invariant of motion is derived. A critical value of the latter sharply separates the domains of loops and boxes and a very simple computation allows to get a clear picture of the distribution of orbits on a given energy surface. Besides, a geometrical representation of the global phase space using the natural surface of section for the problem, the 2D sphere, is presented. This provides a better visualization of the dynamics. In a second part we introduce a new indicator of the basic dynamics, the Mean Exponential Growth factor of Nearby Orbits (MEGNO), that is suitable to investigate the phase space structure associated to a general Hamiltonian. When applied to the 2D logarithmic potential it is shown to be effective to obtain a picture of the global dynamics and, also, to derive good estimates of the largest Lyapunov characteristic number in realistic physical times. Comparisons with other techniques reveal that the MEGNO provides more information about the dynamics in the phase space than other wide used tools. Finally, we discuss the structure of the phase space associated to the 2D logarithmic potential for several values of the semiaxis ratio and energy. We focus our attention on the stability analysis of the principal periodic orbits and on the chaotic component. We obtain critical energy values for which connections between the main stochastic zones take place. In any case, the whole chaotic domain appears to be always confined to narrow filaments, with a Lyapunov time about three characteristic periods.
Facultad de Ciencias Astronómicas y Geofísicas
Materia
Ciencias Astronómicas
Chaos
Galaxies: dynamics
Methods: analytical-numerical
Stellar dynamics
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/83597

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network_acronym_str SEDICI
repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling Simple tools to study global dynamics in non-axisymmetric galactic potentials - ICincotta, Pablo MiguelSimó, C.Ciencias AstronómicasChaosGalaxies: dynamicsMethods: analytical-numericalStellar dynamicsIn a first part we discuss the well-known problem of the motion of a star in a general non-axisymmetric 2D galactic potential by means of a very simple but almost universal system: the pendulum model. It is shown that both loop and box families of orbits arise as a natural consequence of the dynamics of the pendulum. An approximate invariant of motion is derived. A critical value of the latter sharply separates the domains of loops and boxes and a very simple computation allows to get a clear picture of the distribution of orbits on a given energy surface. Besides, a geometrical representation of the global phase space using the natural surface of section for the problem, the 2D sphere, is presented. This provides a better visualization of the dynamics. In a second part we introduce a new indicator of the basic dynamics, the Mean Exponential Growth factor of Nearby Orbits (MEGNO), that is suitable to investigate the phase space structure associated to a general Hamiltonian. When applied to the 2D logarithmic potential it is shown to be effective to obtain a picture of the global dynamics and, also, to derive good estimates of the largest Lyapunov characteristic number in realistic physical times. Comparisons with other techniques reveal that the MEGNO provides more information about the dynamics in the phase space than other wide used tools. Finally, we discuss the structure of the phase space associated to the 2D logarithmic potential for several values of the semiaxis ratio and energy. We focus our attention on the stability analysis of the principal periodic orbits and on the chaotic component. We obtain critical energy values for which connections between the main stochastic zones take place. In any case, the whole chaotic domain appears to be always confined to narrow filaments, with a Lyapunov time about three characteristic periods.Facultad de Ciencias Astronómicas y Geofísicas2000-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf205-228http://sedici.unlp.edu.ar/handle/10915/83597enginfo:eu-repo/semantics/altIdentifier/issn/0365-0138info:eu-repo/semantics/altIdentifier/doi/10.1051/aas:2000108info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T11:15:50Zoai:sedici.unlp.edu.ar:10915/83597Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:15:51.02SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Simple tools to study global dynamics in non-axisymmetric galactic potentials - I
title Simple tools to study global dynamics in non-axisymmetric galactic potentials - I
spellingShingle Simple tools to study global dynamics in non-axisymmetric galactic potentials - I
Cincotta, Pablo Miguel
Ciencias Astronómicas
Chaos
Galaxies: dynamics
Methods: analytical-numerical
Stellar dynamics
title_short Simple tools to study global dynamics in non-axisymmetric galactic potentials - I
title_full Simple tools to study global dynamics in non-axisymmetric galactic potentials - I
title_fullStr Simple tools to study global dynamics in non-axisymmetric galactic potentials - I
title_full_unstemmed Simple tools to study global dynamics in non-axisymmetric galactic potentials - I
title_sort Simple tools to study global dynamics in non-axisymmetric galactic potentials - I
dc.creator.none.fl_str_mv Cincotta, Pablo Miguel
Simó, C.
author Cincotta, Pablo Miguel
author_facet Cincotta, Pablo Miguel
Simó, C.
author_role author
author2 Simó, C.
author2_role author
dc.subject.none.fl_str_mv Ciencias Astronómicas
Chaos
Galaxies: dynamics
Methods: analytical-numerical
Stellar dynamics
topic Ciencias Astronómicas
Chaos
Galaxies: dynamics
Methods: analytical-numerical
Stellar dynamics
dc.description.none.fl_txt_mv In a first part we discuss the well-known problem of the motion of a star in a general non-axisymmetric 2D galactic potential by means of a very simple but almost universal system: the pendulum model. It is shown that both loop and box families of orbits arise as a natural consequence of the dynamics of the pendulum. An approximate invariant of motion is derived. A critical value of the latter sharply separates the domains of loops and boxes and a very simple computation allows to get a clear picture of the distribution of orbits on a given energy surface. Besides, a geometrical representation of the global phase space using the natural surface of section for the problem, the 2D sphere, is presented. This provides a better visualization of the dynamics. In a second part we introduce a new indicator of the basic dynamics, the Mean Exponential Growth factor of Nearby Orbits (MEGNO), that is suitable to investigate the phase space structure associated to a general Hamiltonian. When applied to the 2D logarithmic potential it is shown to be effective to obtain a picture of the global dynamics and, also, to derive good estimates of the largest Lyapunov characteristic number in realistic physical times. Comparisons with other techniques reveal that the MEGNO provides more information about the dynamics in the phase space than other wide used tools. Finally, we discuss the structure of the phase space associated to the 2D logarithmic potential for several values of the semiaxis ratio and energy. We focus our attention on the stability analysis of the principal periodic orbits and on the chaotic component. We obtain critical energy values for which connections between the main stochastic zones take place. In any case, the whole chaotic domain appears to be always confined to narrow filaments, with a Lyapunov time about three characteristic periods.
Facultad de Ciencias Astronómicas y Geofísicas
description In a first part we discuss the well-known problem of the motion of a star in a general non-axisymmetric 2D galactic potential by means of a very simple but almost universal system: the pendulum model. It is shown that both loop and box families of orbits arise as a natural consequence of the dynamics of the pendulum. An approximate invariant of motion is derived. A critical value of the latter sharply separates the domains of loops and boxes and a very simple computation allows to get a clear picture of the distribution of orbits on a given energy surface. Besides, a geometrical representation of the global phase space using the natural surface of section for the problem, the 2D sphere, is presented. This provides a better visualization of the dynamics. In a second part we introduce a new indicator of the basic dynamics, the Mean Exponential Growth factor of Nearby Orbits (MEGNO), that is suitable to investigate the phase space structure associated to a general Hamiltonian. When applied to the 2D logarithmic potential it is shown to be effective to obtain a picture of the global dynamics and, also, to derive good estimates of the largest Lyapunov characteristic number in realistic physical times. Comparisons with other techniques reveal that the MEGNO provides more information about the dynamics in the phase space than other wide used tools. Finally, we discuss the structure of the phase space associated to the 2D logarithmic potential for several values of the semiaxis ratio and energy. We focus our attention on the stability analysis of the principal periodic orbits and on the chaotic component. We obtain critical energy values for which connections between the main stochastic zones take place. In any case, the whole chaotic domain appears to be always confined to narrow filaments, with a Lyapunov time about three characteristic periods.
publishDate 2000
dc.date.none.fl_str_mv 2000-12
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
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info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://sedici.unlp.edu.ar/handle/10915/83597
url http://sedici.unlp.edu.ar/handle/10915/83597
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/0365-0138
info:eu-repo/semantics/altIdentifier/doi/10.1051/aas:2000108
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
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dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
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