框架陀螺仪运动的混沌性态

讨论理想状态下框架支承陀螺仪的运动,列出以框架转角及对应的广义动量为变量的正则方程．应用Melnikov方法和Poincaré截面的数值方法证实,转子对匀速旋转的微小偏离可导致混饨运动出现．数值计算还证实,基座的匀速转动亦可引起陀螺仪的混饨运动．从而表明,实验观测到的陀螺仪随机漂移现象也可来源于内禀随机性,而不仅是外在随机因素的作用结果．

CHAOTIC BEHAVIOR OF GIMBAL GYROSCOPE MOTION

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.