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.

A semi-analytic algorithm for constructing lower dimensional elliptic tori in planetary systems / M. Sansottera, U. Locatelli, A. Giorgilli. - In: CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY. - ISSN 0923-2958. - 111:3(2011), pp. 337-361.

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

M. Sansottera
Primo
;
A. Giorgilli
Ultimo
2011

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.
KAM theory ; Lower dimensional invariant tori ; Normal form methods ; n-body planetary problem ; Hamiltonian systems ; Celestial Mechanics
Settore MAT/07 - Fisica Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/163453
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