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

Details A semi-analytic algorithm for constructing lower dimensional elliptic tori in planetary systems A semi-analytic algorithm for constructing lower dimensional elliptic tori in planetary systems

Nov 2011

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011cemda.111..337s&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 111, Issue 3, pp.337-361

Astronomy and Astrophysics

Astronomy

Scientific paper

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.

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