Stability, Bifurcation and Chaos of a Gyro-Pendulum on a Rotating Basis

The motion of a gyro-pendulum mounted on a rotating basis by a Cardan’s gimbal is discussed in this chapter. The problems on relative equilibrium of the gyro in the gimbal, its stability and bifurcation are studied. The global behavior of gyro’s motion is presented in the parameter space, which shows that the vertical position of gyro’s axis becomes unstable and transforms to a stable position deviated from vertical, when the gyro has a slender shape and the rotor speed is small enough. The numerical calculation of the Poincaré surface of section demonstrates a chaotic behavior of gyro’s motion. It follows that the random drift of gyroscope, which is normally considered as a result of an external stochastic factor, can be caused by the intrinsic stochasticity too. The bifurcation phenomenon can disappear and the chaotic area can be reduced by increasing the rotor speed.