Le problème de Gyldén du point de vue de la théorie KAM

Şelaru, Dan; Mioc, Vasile

doi:10.1016/s1251-8069(97)89451-1

Cited by 2 publications

(1 citation statement)

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“…Mathematically speaking, the Gyldén-type problem with periodically changing ν was approached by us from many standpoints: first-order analytical solutions in the case of a periodic variation of the equivalent gravitational parameter (Ş elaru et al 1992), the slowly-changing equivalent gravitational parameter (Cucu-Dumitrescu & Ş elaru 1997), KAM theory applied to this problem (Ş elaru & Mioc 1997), periodic orbits at infinity and chaotic behavior (Diacu & Ş elaru 1998), etc.…”

Section: Introductionmentioning

confidence: 99%

The Gyldén-type problem revisited: More refined analytical solutions

et al. 2006

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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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Section: Introductionmentioning

confidence: 99%