On the Stability of the Upside-Down Pendulum with Damping

  title={On the Stability of the Upside-Down Pendulum with Damping},
  author={Michele Bartuccelli and Guido Gentile and Konstantinos Georgiou},
A rigorous analysis is presented in order to show that, in 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 byproduct we obtain an analytic expression of the solution for initial data close enough to the equilibrium position. 

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