The Supression of Chaos in Periodically Forced Oscillators

  • Steven W. Shaw
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)


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.


Unstable Manifold Homoclinic Orbit Inverted Pendulum Homoclinic Solution Optimal Input 
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    Moore, D.B.; Shaw, S.W.: “The experimental response of an impacting pendulum system,” Int. J. of Nonlinear Mech., to appear.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Steven W. Shaw
    • 1
  1. 1.Department of Mechanical EngineeringMichigan State UniversityEast LansingUSA

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