Invariant Tori in the Secular Motions of the Three-Body Planetary Systems View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2001

AUTHORS

Ugo Locatelli , Antonio Giorgilli

ABSTRACT

We consider the problem of the applicability of KAM theorem to a realistic problem of three bodies. In the framework of the averaged dynamics over the fast angles for the Sun—Jupiter—Saturn system we can prove the perpetual stability of the orbit. The proof is based on semi-numerical algorithms requiring both explicit algebraic manipulations of series and analytical estimates. The proof is made rigorous by using interval arithmetics in order to control the numerical errors. More... »

PAGES

47-74

References to SciGraph publications

  • 1995-07. Stability of the planetary three-body problem in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1995-07. Stability of the planetary three-body problem in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1997-06. On the Stability of Realistic Three-Body Problems in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2000-05. A Note on a General Algorithm for Two-Body Expansions in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1967-03. Convergent series expansions for quasi-periodic motions in MATHEMATISCHE ANNALEN
  • 1979. Preservation of conditionally periodic movements with small change in the Hamilton function in STOCHASTIC BEHAVIOR IN CLASSICAL AND QUANTUM HAMILTONIAN SYSTEMS
  • 1999. Introduction to Frequency Map Analysis in HAMILTONIAN SYSTEMS WITH THREE OR MORE DEGREES OF FREEDOM
  • 1997-03. Kolmogorov theorem and classical perturbation theory in ZEITSCHRIFT FÜR ANGEWANDTE MATHEMATIK UND PHYSIK
  • Book

    TITLE

    New Developments in the Dynamics of Planetary Systems

    ISBN

    978-90-481-5702-0
    978-94-017-2414-2

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-94-017-2414-2_3

    DOI

    http://dx.doi.org/10.1007/978-94-017-2414-2_3

    DIMENSIONS

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