A semi-analytic algorithm for constructing lower dimensional elliptic tori in planetary systems |
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Authors: | Marco Sansottera Ugo Locatelli Antonio Giorgilli |
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Institution: | 1.Dipartimento di Matematica,Università degli Studi di Milano,Milan,Italy;2.Dipartimento di Matematica,Università degli Studi di Roma “Tor Vergata”,Rome,Italy |
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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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Keywords: | |
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