ALMOST-SURE STABILITY OF A GYROPENDULUM SUBJECTED TO WHITE-NOISE RANDOM SUPPORT MOTION

Instability behaviour of a gyropendulum subjected to white noise vertical support motion is examined. Conditions for almost-sure asymptotic stability are obtained explicitly. A stochastic averaging procedure is employed to evaluate the maximal Lyapunov exponent. The sign of this exponent determines the instability behaviour of this system. Closed-form expressions for the instability conditions obtained in this study are employed to predict the minimum level of damping required to ensure almost-sure asymptotic stability.