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SM ISO690:2012 GADOMSKI, Leszek, GREBENIKOV, Evgenii, JAKUBIAK, Miroslaw, KOZAK-SKOWORODKIN, Dorota. The Lyapunov stability in restricted problems of cosmic dynamics. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2003, nr. 1(41), pp. 7-17. ISSN 1024-7696. |
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica | ||||||
Numărul 1(41) / 2003 / ISSN 1024-7696 /ISSNe 2587-4322 | ||||||
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Pag. 7-17 | ||||||
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Majority of cosmic dynamical problems are described by Hamiltonian
systems. In this case the Lyapunov stability problem is the toughest problem of
qualitative theory, but for two freedom degrees KAM–theory (Kolmogorov–Arnold–
Moser methods) allows for the complete study [1–3]. For application of Arnold–Moser
theorem [4] it is necessary to make finite sequence of Poincar´e–Birkhoff canonical
transformations [5] for Hamiltonian normalization. With the help of Symbolic System
”Mathematica” [6] we determine the conditions of Lyapunov stability and instability
of equilibrium points of restricted n–body problems [7]. |
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Cuvinte-cheie differential equations, stability, equilibrium points, computer algebra, Mathe- matica 4.0 |
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