A modified Gaussian moment closure method for nonlinear stochastic differential equations

Parametric excitation of a nonlinear physical pendulum by modulation of its moment of inertia is analyzed in terms of physics as an example of the suggested approach. The modulation is provided by a redistribution of auxiliary masses. The system is investigated both analytically and with the help of computer simulations. The threshold and other characteristics of parametric resonance are found and discussed in detail. The role of nonlinear properties of the physical system in restricting the resonant swinging is emphasized. Phase locking between the drive and oscillations of the pendulum and the phenomenon of parametric autoresonance are investigated. The boundaries of parametric instability are determined as functions of the modulation depth and the quality factor. The feedback providing active optimal control of amplification and attenuation of oscillations is analyzed. An effective method of suppressing undesirable rotary oscillations of suspended constructions is suggested.