Motion near the 3/1 resonance of the planar elliptic restricted three body problem View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1989-06

AUTHORS

Jacques Henrard, N.D. Caranicolas

ABSTRACT

The global semi-numerical perturbation method proposed by Henrard and Lemaître (1986) for the 2/1 resonance of the planar elliptic restricted three body problem is applied to the 3/1 resonance and is compared with Wisdom's perturbative treatment (1985) of the same problem. It appears that the two methods are comparable in their ability to reproduce the results of numerical integration especially in what concerns the shape and area of chaotic domains. As the global semi-numerical perturbation method is easily adapted to more general types of perturbations, it is hoped that it can serve as the basis for the analysis of more refined models of asteroidal motion. We point out in our analysis that Wisdom's uncertainty zone mechanism for generating chaotic domains (also analysed by Escande 1985 under the name of slow Hamiltonian chaotic layer) is not the only one at work in this problem. The secondary resonance ωp = 0 plays also its role which is qualitatively (if not quantitatively) important as it is closely associated with the random jumps between a high eccentricity mode and a low eccentricity mode. More... »

PAGES

99-121

References to SciGraph publications

  • 1986-02. Canonical solution of the two critical argument problem in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1986-09. A perturbation method for problems with two critical arguments in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1899-07. Les méthodes nouvelles de la mécanique céleste in IL NUOVO CIMENTO (1895-1900)
  • 1984-02. A simple derivation of capture probabilities for the J+1:J and J+2:J orbit-orbit resonance problems in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1984-04. Motion of two planets with periods commensurable in the ratio 2∶1 solutions of the hori auxiliary system in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1988. Resonances in the Planar Elliptic Restricted Problem in LONG-TERM DYNAMICAL BEHAVIOUR OF NATURAL AND ARTIFICIAL N-BODY SYSTEMS
  • 1986-04. The reducing transformation and Apocentric Librators in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1984-02. High-order resonances in the restricted three-body problem in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf00051201

    DOI

    http://dx.doi.org/10.1007/bf00051201

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1046842398


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