Asymptotic Solution of the Autoresonance Problem |
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Authors: | L. A. Kalyakin |
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Affiliation: | (1) Ufa Scientific Center, Institute of Mathematics, RAS, Ufa, Russia |
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Abstract: | We study the problem of forced oscillations near a stable equilibrium of a two-dimensional nonlinear Hamiltonian system of equations. A given exciting force is represented as rapid oscillations with a small amplitude and a slowly varying frequency. We study the conditions under which such a perturbation makes the phase trajectory of the system recede from the original equilibrium point to a distance of the order of unity. To study the problem, we construct asymptotic solutions using a small amplitude parameter. We present the solution for not-too-small values of time outside the original boundary layer. |
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Keywords: | nonlinear oscillations resonance asymptotic approximation averaging |
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