Base vibration influence on the gyro pendulum precession motion

The task about research the behavior of the gyro pendulum fixing on the vibration base in case when the action of the vibration is substituted with vibration (dynamic) force is envisaged. As always, the motion of gyroscope on vibration base is described by simultaneous differential equations with variable coefficients. The last one makes difficult finding the gyroscope motion law. But received results on substitution the action of linear vibration on the pendulum simultaneousness on dynamic force determined vibration base kinetic energy. That makes possible the substitution of simultaneous differential equations with variable coefficients on simultaneous differential equations with constant coefficients. Also some results of experimental research of pendulum systems in harmonic base vibration are adduced. The results of theoretical and experimental research show that precession of gyro pendulum has different value for case when gyro pendulum center of gravity is displaced up and for case when pendulum center of gravity is displaced down. In first cause we observed precession value reduction and under certain conditions (when the value of vibration force is equal to force of gravity) it value can be equal to zero. For the second cause precession value precession increases