A semi-analytic algorithm for constructing lower dimensional elliptic tori in planetary systems View Full Text


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Article Info

DATE

2011-11

AUTHORS

Marco Sansottera, Ugo Locatelli, Antonio Giorgilli

ABSTRACT

We adapt the Kolmogorov’s normalization algorithm (which is the key element of the original proof scheme of the KAM theorem) to the construction of a suitable normal form related to an invariant elliptic torus. As a byproduct, our procedure can also provide some analytic expansions of the motions on elliptic tori. By extensively using algebraic manipulations on a computer, we explicitly apply our method to a planar four-body model not too different with respect to the real Sun–Jupiter–Saturn–Uranus system. The frequency analysis method allows us to check that our location of the initial conditions on an invariant elliptic torus is really accurate. More... »

PAGES

337

References to SciGraph publications

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  • 2000-01. On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
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  • 1995. Quantitative Methods in Classical Perturbation Theory in FROM NEWTON TO CHAOS
  • 2001-05. High order symplectic integrators for perturbed Hamiltonian systems in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1971-07. Existence of quasi-periodic solutions to the three-body problem in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 2003-11. Elliptic Two-Dimensional Invariant Tori for the Planetary Three-Body Problem in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 2009-06. Kolmogorov and Nekhoroshev theory for the problem of three bodies in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 2002-11. Partial Reduction in the N-Body Planetary Problem using the Angular Momentum Integral in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1999. Introduction to Frequency Map Analysis in HAMILTONIAN SYSTEMS WITH THREE OR MORE DEGREES OF FREEDOM
  • 1997-10. On the Persistence of Lower Dimensional Invariant Tori under Quasi-Periodic Perturbations in JOURNAL OF NONLINEAR SCIENCE
  • 1989-12. On elliptic lower dimensional tori in hamiltonian systems in MATHEMATISCHE ZEITSCHRIFT
  • 1984-02. A proof of Kolmogorov’s theorem on invariant tori using canonical transformations defined by the Lie method in IL NUOVO CIMENTO B (1971-1996)
  • 1997-03. Kolmogorov theorem and classical perturbation theory in ZEITSCHRIFT FÜR ANGEWANDTE MATHEMATIK UND PHYSIK
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10569-011-9375-x

    DOI

    http://dx.doi.org/10.1007/s10569-011-9375-x

    DIMENSIONS

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