A semi-analytic algorithm for constructing lower dimensional elliptic tori in planetary systems
Articolo
Data di Pubblicazione:
2011
Citazione:
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.
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.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
KAM theory ; Lower dimensional invariant tori ; Normal form methods ; n-body planetary problem ; Hamiltonian systems ; Celestial Mechanics
Elenco autori:
M. Sansottera, U. Locatelli, A. Giorgilli
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