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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2003, Number 1, Pages 7–17
(Mi basm183)
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Research articles
The Lyapunov stability in restricted problems of cosmic dynamics
L. Gadomskii, E. Grebenikov, M. Jakubiak, D. Kozak–Skoworodkin University of Podlasie, Siedlce, Poland
Abstract:
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 Poincaré–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].
Keywords and phrases:
differential equations, stability, computer algebra, Mathematica 4.0, equilibrium points.
Received: 04.11.2002
Citation:
L. Gadomskii, E. Grebenikov, M. Jakubiak, D. Kozak–Skoworodkin, “The Lyapunov stability in restricted problems of cosmic dynamics”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2003, no. 1, 7–17
Linking options:
https://www.mathnet.ru/eng/basm183 https://www.mathnet.ru/eng/basm/y2003/i1/p7
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Abstract page: | 234 | Full-text PDF : | 59 | References: | 51 | First page: | 1 |
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