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arXiv · 1010.2617

A Semi-Analytic Algorithm for Constructing Lower Dimensional Elliptic Tori in Planetary Systems

Marco Sansottera·Ugo Locatelli·Antonio Giorgilli
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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.

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Marco Sansottera, Ugo Locatelli, Antonio Giorgilli. 2010-10-13. A Semi-Analytic Algorithm for Constructing Lower Dimensional Elliptic Tori in Planetary Systems. https://doi.org/10.1007/s10569-011-9375-x

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