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Non-linear Oscillations of a Hamiltonian System with One and Half Degrees of Freedom
B. S. Bardina, A. J. Maciejewskib a Department of Theoretical Mechanics,
Faculty of Applied Mathematics,
Moscow Aviation Institute,
Moscow, Russia
b Toruń Centre for Astronomy, N.Copernicus University,
87-100 Toruń, Gagarina 11, Poland
Аннотация:
We study non-linear oscillations of a nearly integrable Hamiltonian system with one and half degrees of freedom in a neighborhood of an equilibrium. We analyse the resonance case of order one. We perform careful analysis of a small finite neighborhood of the equilibrium. We show that in the case considered the equilibrium is not stable, however, this instability is soft, i.e. trajectories of the system starting near the equilibrium remain close to it for an infinite period of time. We discuss also the effect of separatrices splitting occurring in the system. We apply our theory to study the motion of a particle in a field of waves packet.
Поступила в редакцию: 09.06.2000
Образец цитирования:
B. S. Bardin, A. J. Maciejewski, “Non-linear Oscillations of a Hamiltonian System with One and Half Degrees of Freedom”, Regul. Chaotic Dyn., 5:3 (2000), 345–360
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd884 https://www.mathnet.ru/rus/rcd/v5/i3/p345
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