Stability of the Planetary Three-Body Problem. II. KAM Theory and Existence of Quasiperiodic Motions

Details Stability of the Planetary Three-Body Problem. II. KAM Theory and Existence of Quasiperiodic Motions Stability of the Planetary Three-Body Problem. II. KAM Theory and Existence of Quasiperiodic Motions

Jul 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995cemda..62..219r&link_type=abstract

Celestial Mechanics & Dynamical Astronomy, Volume 62, Issue 3, pp.219-261

Astronomy and Astrophysics

Astronomy

23

Planetary Motion, Perturbation Theory, Kam Theory, Celestial Mechanics, Stability Of Planetary System

Scientific paper

Using new expansions of the planetary Hamiltonian in Poincaré canonical elliptic variables, Arnold's theorem for the existence of quasiperiodic orbits in degenerated cases is applied to the general spatial planetary three body problem. The existence of quasiperiodic motion is demonstrated for almost all values of the ratio of semi-major axis α in ]0, 0.8] and almost all values of the mutual inclination up to about 1 degree. This extends the previous result of Arnold (1963).

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