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Zbl 0908.70018
Schmitt, John M.; Bayly, Philip V.
Bifurcations in the mean angle of a horizontally shaken pendulum: Analysis and experiment. (English)
[J] Nonlinear Dyn. 15, No.1, 1-14 (1998). ISSN 0924-090X; ISSN 1573-269X/e

Summary: 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 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.

MSC 2000:: *70K20 Stability of nonlinear oscillations (general mechanics)
70K40 Forced motions (general mechanics)
70-05 Experimental papers (mechanics of particles and systems)

Keywords: method of multiple time scales; pitchfork bifurcation; saddle-node bifurcation

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