The Gyldén problem from the standpoint of KAM theory.

Details The Gyldén problem from the standpoint of KAM theory. The Gyldén problem from the standpoint of KAM theory.

Oct 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997crasb.325..487s&link_type=abstract

Comptes Rendus de l'Academie des Sciences, Sér. II, Fasc. b, Tome 325, No. 8, p. 487 - 490

Astronomy and Astrophysics

Astronomy

1

Two-Body Problem: Perturbation Theory

Scientific paper

The Gyldén problem (the two-body problem with changing gravitational parameter) is being tackled in Hamiltonian formalism, in the most interesting case (astronomically and physically), that of a periodic perturbation. Using the angular momentum conservation, the number of degrees of freedom is reduced to one and a half, allowing the application of the KAM theory after a classical extension of the phase space. The Hamiltonian does not satisfy the usual KAM condition for nondegeneracy, but fulfils that for isoenergetic nondegeneracy. These facts allow the authors to formulate important conclusions concerning the behaviour of the system.

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