CHAOTIC BEHAVIOR OF GIMBAL GYROSCOPE MOTION
框架陀螺仪运动的混沌性态

The motion of a gimbal gyroscope is discussed in the present paper. The gyroscopeis composed of gimbles and rotor, and is regarded as a Hamilton system when the mass centersof gimbals and rotor coincide with the center of suspension and the bearings of gimbals are idealconstraints. The Hamilton's canonical equations with the rotational angles of gimbals and itsgeneralized momentums as variables are derived. When the spin of rotor is slightly deviated fromthe stationary rotation with uniform speed, the gimbals may perform a chaotic motion, which canbe predicted by using the Melnikov's method and verified by numerical calculation of the Poincaresurface of section. In another case when the base of gyroscope rotates uniformly, the chaoticbehavior of gimbal's motion can be demonstrated by the Poincare maps too. It is shown that thegyro's random drift phenomenon observed in the experiment can also be caused by the intrinsicstochasticity in addition to the action of external stochastic factors.