Parametric and Autoparametric Resonance |
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Authors: | Ferdinand Verhulst |
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Institution: | (1) Mathematisch Instituut, University of Utrecht, PO Box 80.010, 3508 TA Utrecht, The Netherlands |
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Abstract: | A large number of mathematical questions are related to problems of parametric and autoparametric resonance in engineering models. The linearized problems generally produce systems of differential equations with periodic coefficients with special stability and genericity questions. We start by reviewing linear systems while discussing normal form techniques and bifurcation results. The linear and nonlinear analysis is illustrated in three cases: rotor dynamics, autoparametric resonance of a parametric oscillator and autoparametric resonance of a self-excited oscillator. In all cases bifurcations, symmetry considerations and attraction to nonclassical limit sets play a part. |
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Keywords: | nonlinear parametric resonance bifurcation |
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