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Bifurcations in the mean angle of a horizontally shaken pendulum: Analysis and experiment. (English) Zbl 0908.70018
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:
70K20Stability of nonlinear oscillations (general mechanics)
70K40Forced nonlinear motions (general mechanics)
70-05Experimental work (mechanics of particles and systems)