A Fundamental Model and Numerical Investigations for the Resonances of the Gyldén Problem

Details A Fundamental Model and Numerical Investigations for the Resonances of the Gyldén Problem A Fundamental Model and Numerical Investigations for the Resonances of the Gyldén Problem

May 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007padeu..19...81c&link_type=abstract

Publications of the Astronomy Department of the Eötvös University (PADEU), 2007, ISBN 963 463 557, Vol. 19. Edited by B. Érdi a

Astronomy and Astrophysics

Astronomy

Scientific paper

We tackle the Gyldén-type problem (a two-body problem with time-changing equivalent gravitational parameter). For the most interesting case for astronomy: small-amplitude periodic variation, we study the behavior of the system in the neighborhood of resonances. We adopt the most realistic astronomical situation: only one dominant term of the Hamiltonian. In this case we point out a fundamental model of resonance, common to every resonant situation, and, moreover, identical to the so-called first model of resonance (Breiter 2003). Considering the simplest case of the variation, we perform some numerical experiments. Even in this simplest case, the phase portraits are very complex: a mixture of oscillation zones, circulation zones and chaotic zones.

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