Nonlinear Dynamics

, Volume 15, Issue 1, pp 1–14

Bifurcations in the Mean Angle of a Horizontally Shaken Pendulum: Analysis and Experiment

  • John M. Schmitt
  • Philip V. Bayly

DOI: 10.1023/A:1008279910762

Cite this article as:
Schmitt, J.M. & Bayly, P.V. Nonlinear Dynamics (1998) 15: 1. doi:10.1023/A:1008279910762


A pendulum excited by high-frequency horizontal displacement of its pivot point will vibrate with small amplitude about a mean position. The mean value is zero for small excitation amplitudes, but if the excitation is large enough the mean angle can take on non-zero values. This behavior is analyzed using the method of multiple time scales. The change in the mean angle is shown to be the result of a pitchfork bifurcation, or a saddle-node bifurcation if the system is imperfect. Analytical predictions of the mean angle as a function of frequency and amplitude are confirmed by physical experiment and numerical simulation.

Pendulumbifurcationpitchforksaddle node

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • John M. Schmitt
    • 1
  • Philip V. Bayly
    • 1
  1. 1.Mechanical Engineering DepartmentWashington UniversitySt. LouisU.S.A.