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


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Article Info

DATE

2000-09

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
  • 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
  • 1997-06. On the Stability of Realistic Three-Body Problems in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 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
  • Identifiers

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    http://scigraph.springernature.com/pub.10.1023/a:1011139523256

    DOI

    http://dx.doi.org/10.1023/a:1011139523256

    DIMENSIONS

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