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On the Stability of the Upside-down Pendulum with Damping

M. V. Bartuccelli, G. Gentile and K. V. Georgiou
Proceedings: Mathematical, Physical and Engineering Sciences
Vol. 458, No. 2018 (Feb. 8, 2002), pp. 255-269
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/3067344
Page Count: 15
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
On the Stability of the Upside-down Pendulum with Damping
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Abstract

A rigorous analysis is presented in order to show that, in the presence of friction, the upward equilibrium position of the vertically driven pendulum, with a small non-vanishing damping term, becomes asymptotically stable when the period of the forcing is below an appropriate threshold value. As a by-product we obtain an analytic expression of the solution for initial data close enough to the equilibrium position.

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