On the Stability of a Periodic Hamiltonian System with One Degree of Freedom in a Transcendental Case |
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Authors: | B S Bardin |
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Institution: | 1.Moscow Aviation Institute (National Research University),Moscow,Russia;2.Mechanical Engineering Research Institute,Russian Academy of Sciences,Moscow,Russia |
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Abstract: | The stability of an equilibrium of a nonautonomous Hamiltonian system with one degree of freedom whose Hamiltonian function depends 2π-periodically on time and is analytic near the equilibrium is considered. The multipliers of the system linearized around the equilibrium are assumed to be multiple and equal to 1 or–1. Sufficient conditions are found under which a transcendental case occurs, i.e., stability cannot be determined by analyzing the finite-power terms in the series expansion of the Hamiltonian about the equilibrium. The equilibrium is proved to be unstable in the transcendental case. |
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