The Gyldén-type problem revisited: More refined analytical solutions

Details The Gyldén-type problem revisited: More refined analytical solutions The Gyldén-type problem revisited: More refined analytical solutions

May 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006an....327..304p&link_type=abstract

Astronomische Nachrichten, Vol.237, Issue 4, p.304

Astronomy and Astrophysics

Astronomy

1

Celestial Mechanics, Stellar Dynamics, Methods: Analytical

Scientific paper

We resume and consistently extend our previous researches concerning the Gyldén-type problem (a two-body problem with time-dependent equivalent gravitational parameter). To approach most of the concrete astronomical situations to be modelled in this way, we consider a periodic small perturbation. For the nonresonant case, we present a second-order analytical solution. For the resonant case, 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 first fundamental model of resonance. Considering the simplest model of periodic change of the equivalent gravitational parameter, we find that all possible resonances are confined to the first fundamental model.

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