This article is cited in 25 papers

150th anniversary of H. Poincaré

Construction of Kolmogorov's normal form for a planetary system

U. Locatelli^a, A. Giorgilli<sup>b

a</sup> Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata", Via della Ricerca Scientifica 1, 00133 Roma, Italy
^b Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano Bicocca, Via R. Cozzi 53, 20125 Milano, Italy

Abstract: We describe an algorithm constructing an invariant KAM torus for a class of planetary systems, such that the mutual attractions, the eccentricities and the inclinations of the planets are small enough. By using computer algebra, we explicitly implement this algorithm for approximating a KAM torus for the problem of three bodies in a case similar to the Sun–Jupiter–Saturn system. We show that, by reducing the masses of the planets by a factor 10 and with a small displacement of the orbits, our semianalytical construction of the torus turns out to be successful.

Keywords: three-body problem, $n$-body problem, KAM theory, perturbation methods, Hamiltonian systems, celestial mechanics.

MSC: 70F07, 70F10, 37J40, 37N05, 70–08, 70H08

Received: 06.04.2005
Accepted: 03.06.2005

Language: English

DOI: 10.1070/RD2005v010n02ABEH000309

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