The Supression of Chaos in Periodically Forced Oscillators
A method for suppressing chaos in a class of periodically forced oscillators is presented. The method involves the manipulation of higher harmonics in the periodic excitation such that the homoclinic tangles which lie at the heart of the chaos are destroyed. The procedure is demonstrated via a particular example: an inverted pendulum with amplitude constraints subjected to periodic base excitation. The general theory is developed using a Melnikov type method (see [1–3] and is supported by some experimental evidence.
KeywordsManifold Librium Alan Shoe
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- 1.Melnikov, V.K.: “On the stability of the center for time periodic perturbations,” Trans. Moscow Math. Soc. 12 1 - 57, 1963.Google Scholar
- 2.Guckenheimer, J.; Holmes, P.: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. 2nd printing, Springer Verlag, New York, Berlin, Heidelberg, Tokyo, 1986.Google Scholar
- 3.Wiggins, S.: Global Bifurcations and Chaos-Analytical Methods, Springer, Verlag, New York, Berlin, Heidelberg, Tokyo, 1988.Google Scholar
- 7.Moore, D.B.; Shaw, S.W.: “The experimental response of an impacting pendulum system,” Int. J. of Nonlinear Mech., to appear.Google Scholar