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Multiple-Nodding Oscillations of a Driven Inverted Pendulum

D. J. Acheson
Proceedings: Mathematical and Physical Sciences
Vol. 448, No. 1932 (Jan. 9, 1995), pp. 89-95
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/52505
Page Count: 7
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Multiple-Nodding Oscillations of a Driven Inverted Pendulum
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Abstract

It has long been known that a simple rigid pendulum can be stabilized against small disturbances in its upside-down state by rapid vertical oscillations of its pivot. Over part of the parameter range for which this happens we find that there is a second, quite different way in which the pendulum can avoid falling over, namely by getting trapped in a limit cycle oscillation about the upward vertical. Each upside-down oscillation of this kind has a distinctive `multiple-nodding' character.

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