We consider the problem of the applicability of KAM theorem to a realistic problem of three bodies. In the framework of the averaged dynamics over the fast angles for the Sun–Jupiter– Saturn system we can prove the perpetual stability of the orbit. The proof is based on semi-numerical algorithms requiring both explicit algebraic manipulations of series and analytical estimates. The proof is made rigorous by using interval arithmetics in order to control the numerical errors.
Locatelli, U., Giorgilli, A. (2000). Invariant tori in the secular motions of the three-body planetary systems. CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 78, 47-74 [10.1023/A:1011139523256].
Invariant tori in the secular motions of the three-body planetary systems
LOCATELLI, UGO;
2000-01-01
Abstract
We consider the problem of the applicability of KAM theorem to a realistic problem of three bodies. In the framework of the averaged dynamics over the fast angles for the Sun–Jupiter– Saturn system we can prove the perpetual stability of the orbit. The proof is based on semi-numerical algorithms requiring both explicit algebraic manipulations of series and analytical estimates. The proof is made rigorous by using interval arithmetics in order to control the numerical errors.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
