Sweeping through a second order resonance View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1988

AUTHORS

Jacques Henrard , Anne de Vleeschauwer

ABSTRACT

The adiabatic invariant theory and its extension to the case of separatrix crossing have been instrumental in setting up simple models describing the effects of the passage through a first order resonance forced by small non conservative forces. These models have been helpful in understanding the processes of capture into resonance and of formation of gaps at resonances. Second order resonances (3/1 or 5/3 …) have not been so thoroughly investigated and present some special features. We shall show how to “disencumber” first the problem from its secular term and how to modelize the “mixed resonance” term involving the sum of the resonant angles. A modelization of the two single satellite resonant terms has already been proposed by Lemaître and Borderies and Goldreich. We shall then assemble those three simple models to show the effect of a passage through the resonance under the assumption that the natural precession rates are large enough for the three individual resonances to be sufficiently separated. More... »

PAGES

99-112

References to SciGraph publications

  • 1986-09. A perturbation method for problems with two critical arguments in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 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
  • 1988-12. Note on the reducing transformation and secular coupling in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1983-07. Secular orbit-orbit resonance between two satellites with non-zero masses in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1982-01. Asymptotic series for planetary motion in periodic terms in three dimensions in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1987-09. Colombo's top in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1984-02. High-order resonances in the restricted three-body problem in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • Book

    TITLE

    Long Term Evolution of Planetary Systems

    ISBN

    978-94-010-7525-1
    978-94-009-2285-3

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-94-009-2285-3_8

    DOI

    http://dx.doi.org/10.1007/978-94-009-2285-3_8

    DIMENSIONS

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