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 nonvanishing 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.
BARTUCCELLI M., V., Gentile, G., Georgiou, K.V. (2002). On the stability of the upside-down pendulum with damping. PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON. SERIES A, 458, 255-269 [10.1098/rspa.2001.0859].
On the stability of the upside-down pendulum with damping
GENTILE, Guido;
2002-01-01
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 nonvanishing 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.File in questo prodotto:
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