Resonance and chaos: I. First-order interior resonances
Autor(a) principal: | |
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Data de Publicação: | 1997 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://aa.springer.de/bibs/7319001/2300290/small.htm http://hdl.handle.net/11449/65046 |
Resumo: | Analytical models for studying the dynamical behaviour of objects near interior, mean motion resonances are reviewed in the context of the planar, circular, restricted threebody problem. The predicted widths of the resonances are compared with the results of numerical integrations using Poincaré surfaces of section with a mass ratio of 10-3 (similar to the Jupiter-Sun case). It is shown that for very low eccentricities the phase space between the 2:1 and 3:2 resonances is predominantly regular, contrary to simple theoretical predictions based on overlapping resonance. A numerical study of the 'evolution' of the stable equilibrium point of the 3:2 resonance as a function of the Jacobi constant shows how apocentric libration at the 2:1 resonance arises; there is evidence of a similar mechanism being responsible for the centre of the 4:3 resonance evolving towards 3:2 apocentric libration. This effect is due to perturbations from other resonances and demonstrates that resonances cannot be considered in isolation. On theoretical grounds the maximum libration width of first-order resonances should increase as the orbit of the perturbing secondary is approached. However, in reality the width decreases due to the chaotic effect of nearby resonances. |
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Resonance and chaos: I. First-order interior resonancesCelestial mechanicsChaosMinor planetsAnalytical models for studying the dynamical behaviour of objects near interior, mean motion resonances are reviewed in the context of the planar, circular, restricted threebody problem. The predicted widths of the resonances are compared with the results of numerical integrations using Poincaré surfaces of section with a mass ratio of 10-3 (similar to the Jupiter-Sun case). It is shown that for very low eccentricities the phase space between the 2:1 and 3:2 resonances is predominantly regular, contrary to simple theoretical predictions based on overlapping resonance. A numerical study of the 'evolution' of the stable equilibrium point of the 3:2 resonance as a function of the Jacobi constant shows how apocentric libration at the 2:1 resonance arises; there is evidence of a similar mechanism being responsible for the centre of the 4:3 resonance evolving towards 3:2 apocentric libration. This effect is due to perturbations from other resonances and demonstrates that resonances cannot be considered in isolation. On theoretical grounds the maximum libration width of first-order resonances should increase as the orbit of the perturbing secondary is approached. However, in reality the width decreases due to the chaotic effect of nearby resonances.Grupo Dinamica Orbital Planetologia Campus Guaratinguetá UNESP, CP 205, Guaratingueta, São PauloAstronomy Unit Queen Mary and Westfield College University of London, Mile End Road, London E1 4NSGrupo Dinamica Orbital Planetologia Campus Guaratinguetá UNESP, CP 205, Guaratingueta, São PauloUniversidade Estadual Paulista (Unesp)University of LondonWinter, O. C. [UNESP]Murray, C. D.2014-05-27T11:18:12Z2014-05-27T11:18:12Z1997-03-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article290-304application/pdfhttp://aa.springer.de/bibs/7319001/2300290/small.htmAstronomy and Astrophysics, v. 319, n. 1, p. 290-304, 1997.0004-6361http://hdl.handle.net/11449/650462-s2.0-00051955232-s2.0-0005195523.pdf0960024575647258Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengAstronomy and Astrophysics2,265info:eu-repo/semantics/openAccess2023-11-19T06:15:05Zoai:repositorio.unesp.br:11449/65046Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462023-11-19T06:15:05Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Resonance and chaos: I. First-order interior resonances |
title |
Resonance and chaos: I. First-order interior resonances |
spellingShingle |
Resonance and chaos: I. First-order interior resonances Winter, O. C. [UNESP] Celestial mechanics Chaos Minor planets |
title_short |
Resonance and chaos: I. First-order interior resonances |
title_full |
Resonance and chaos: I. First-order interior resonances |
title_fullStr |
Resonance and chaos: I. First-order interior resonances |
title_full_unstemmed |
Resonance and chaos: I. First-order interior resonances |
title_sort |
Resonance and chaos: I. First-order interior resonances |
author |
Winter, O. C. [UNESP] |
author_facet |
Winter, O. C. [UNESP] Murray, C. D. |
author_role |
author |
author2 |
Murray, C. D. |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) University of London |
dc.contributor.author.fl_str_mv |
Winter, O. C. [UNESP] Murray, C. D. |
dc.subject.por.fl_str_mv |
Celestial mechanics Chaos Minor planets |
topic |
Celestial mechanics Chaos Minor planets |
description |
Analytical models for studying the dynamical behaviour of objects near interior, mean motion resonances are reviewed in the context of the planar, circular, restricted threebody problem. The predicted widths of the resonances are compared with the results of numerical integrations using Poincaré surfaces of section with a mass ratio of 10-3 (similar to the Jupiter-Sun case). It is shown that for very low eccentricities the phase space between the 2:1 and 3:2 resonances is predominantly regular, contrary to simple theoretical predictions based on overlapping resonance. A numerical study of the 'evolution' of the stable equilibrium point of the 3:2 resonance as a function of the Jacobi constant shows how apocentric libration at the 2:1 resonance arises; there is evidence of a similar mechanism being responsible for the centre of the 4:3 resonance evolving towards 3:2 apocentric libration. This effect is due to perturbations from other resonances and demonstrates that resonances cannot be considered in isolation. On theoretical grounds the maximum libration width of first-order resonances should increase as the orbit of the perturbing secondary is approached. However, in reality the width decreases due to the chaotic effect of nearby resonances. |
publishDate |
1997 |
dc.date.none.fl_str_mv |
1997-03-01 2014-05-27T11:18:12Z 2014-05-27T11:18:12Z |
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://aa.springer.de/bibs/7319001/2300290/small.htm Astronomy and Astrophysics, v. 319, n. 1, p. 290-304, 1997. 0004-6361 http://hdl.handle.net/11449/65046 2-s2.0-0005195523 2-s2.0-0005195523.pdf 0960024575647258 |
url |
http://aa.springer.de/bibs/7319001/2300290/small.htm http://hdl.handle.net/11449/65046 |
identifier_str_mv |
Astronomy and Astrophysics, v. 319, n. 1, p. 290-304, 1997. 0004-6361 2-s2.0-0005195523 2-s2.0-0005195523.pdf 0960024575647258 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Astronomy and Astrophysics 2,265 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
290-304 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_ |
1799964998249742336 |