Nonlinear Dynamics

, Volume 23, Issue 4, pp 335–352 | Cite as

Numerical Study of a Forced Pendulum with Friction

  • C.-H. Lamarque
  • J. Bastien


We first describe the model of a forced pendulum with viscousdamping and Coulomb friction. Then we show that a unique local solutionof the mathematically well-posed problem exists. An adapted numericalscheme is built. Attention is devoted to the study of the nonlinearbehaviour of a pendulum via a numerical scheme with small constant timesteps. We describe the global behaviour of the free and forcedoscillations of the pendulum due to friction. We show that chaoticbehaviour occurs when friction is not too large. Lyapunov exponents arecomputed and a Melnikov relation is obtained as a limit of regularisedCoulomb friction. For larger friction, asymptotic behaviour correspondsto equilibrium.

Coulomb friction implicit Euler method numerical scheme maximal monotone operator pendulum chaos vibrations 


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Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • C.-H. Lamarque
    • 1
  • J. Bastien
    • 1
  1. 1.Ecole Nationale des Travaux Publics de l'EtatLGM – URA CNRS 1652Vaulx-en-Velin CedexFrance

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