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.

Sansottera, M., Giorgilli, A., Locatelli, U. (2011). A semi-analytic algorithm for constructing lower dimensional elliptic tori in planetary systems. CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 111, 337-361 [10.1007/s10569-011-9375-x].

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

LOCATELLI, UGO
2011-01-01

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.
2011
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/07 - FISICA MATEMATICA
English
Con Impact Factor ISI
http://link.springer.com/article/10.1007/s10569-011-9375-x
Sansottera, M., Giorgilli, A., Locatelli, U. (2011). A semi-analytic algorithm for constructing lower dimensional elliptic tori in planetary systems. CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 111, 337-361 [10.1007/s10569-011-9375-x].
Sansottera, M; Giorgilli, A; Locatelli, U
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/102819
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