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Preprints of the Keldysh Institute of Applied Mathematics, 2000, 051
(Mi ipmp1196)
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Families of Periodic Solutions of the Beletskii Equation
A. D. Bruno
Abstract:
We give a survey of achievements in the study of planar periodic oscillations and rotations of a satellite around its masscenter that moves along the elliptic orbit in the central gravitational field. These oscillations and rotations are described by the ordinary differential (Beletskii) equation of the second order with periodic coefficients and two parameters. The equation is equivalent to the periodic Hamiltonian system with one degree of freedom and has a singularity. It appeared that two-parameter families of generalized periodic solutions of the simple equation have the unexpectedly complicated structure. In particular, near the singularity of the equation these families form the very complicated structures of a new type.
Citation:
A. D. Bruno, “Families of Periodic Solutions of the Beletskii Equation”, Keldysh Institute preprints, 2000, 051
Linking options:
https://www.mathnet.ru/eng/ipmp1196 https://www.mathnet.ru/eng/ipmp/y2000/p51
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Statistics & downloads: |
Abstract page: | 116 | Full-text PDF : | 18 |
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