Approximate analytical solutions for oscillatory and rotational motion of a parametric pendulum

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In this paper, the authors have studied dynamic responses of a parametric pendulum by means of analytical methods. The fundamental resonance structure was determined by looking at the undamped case. The two typical responses, oscillations and rotations, were investigated by applying perturbation methods. The primary resonance boundaries for oscillations and pure rotations were computed, and the approximate analytical solutions for small oscillations and period-one rotations were obtained. The solution for the rotations has been derived for the first time. Comparisons between the analytical and numerical results show good agreements.

Original languageEnglish
Pages (from-to)311-320
Number of pages10
JournalNonlinear Dynamics
Issue number1-3
Early online date1 Nov 2006
Publication statusPublished - Jan 2007


  • parametric pendulum
  • nonlinear dynamical system
  • perturbation method
  • oscillations
  • rotations
  • excited pendulum
  • forced pendulum
  • nonlinear oscillators
  • symmetry-breaking
  • orbits

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