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The Gyldén‐type problem revisited: More refined analytical solutions
Author(s) -
Pal A.,
Şelaru D.,
Mioc V.,
CucuDumitrescu C.
Publication year - 2006
Publication title -
astronomische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.394
H-Index - 63
eISSN - 1521-3994
pISSN - 0004-6337
DOI - 10.1002/asna.200510537
Subject(s) - physics , hamiltonian (control theory) , perturbation (astronomy) , type (biology) , gravitation , first order , term (time) , resonance (particle physics) , mathematical physics , classical mechanics , theoretical physics , mathematics , quantum mechanics , mathematical optimization , ecology , biology
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 .nd that all possible resonances are con.ned to the first fundamental model. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)