Stability of a Parametrically Excited Damped Inverted Pendulum


Erdos, G., & Singh, T.


Journal of Sound and Vibrations, 198(5), 643-650, 1996.


A perturbation approach was used to arrive at a closed-form solution for the stability surface of a damped inverted pendulum. A recursive solution was used to arrive at the period-advanced map whose eigenvalues determine the stability of the system. Results show that the system is not a strong function of damping in the system. However, at larger damping, the amplitude of forcing for a given frequency increases significantly compared to the undamped case. Numerical simulations of the nonlinear system are used to corroborate that the stability border predicted by linearized approximation is reliable. The solution for the undamped case which is a special case of the damped system was shown to closely approach that determined by Landau and Lifshitz.

   Author = {Erdos, G., T. Singh},
   Journal = {Journal of Sound and Vibrations},
   Month = {Dec.},
   Pages = {643-650},
   Title = {Stability of a Parametrically Excited Damped Inverted Pendulum},
   Volume = {198},
   Number = {5},
   Year = {1996}