Regular and singular periodic perturbations of an oscillator with cubic restoring force |
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Authors: | Yu N Bibikov V R Bukaty A A Dorodenkov |
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Institution: | 1.St. Petersburg State University,St. Petersburg,Russia;2.St. Petersburg State Engineering Institute,St. Petersburg,Russia |
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Abstract: | The paper considers small periodic regular and singular perturbations of a system, whose conservative part is an oscillator
with cubic restoring force. The smallness of perturbations is due to both the smallness of the neighborhood of equilibrium
and the presence of a small parameter. In the absence of a small parameter, we obtain conditions for Lyapunov stability of
the equilibrium position. If a small parameter is present, we derive (both for regular and singular perturbations) an equation
whose positive roots are in correspondence with invariant two-dimensional tori of the perturbed system. |
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Keywords: | |
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