Optimization Analysis on Gyroscope’s Three Dimensions Complicated Motion and Lash-Force

Abstract

The complicated motion of the gyroscope includes the rotation, the precession, the nutation and the sliding motion which are coupled, and it is affected by the lash-force by the whip. Taking the gyroscope which is moving stably as the research subject, according to the motion characteristics of the gyro’s rotation and precession, the gyro is assumed to be the two-force bar, and the coupled relationship of the gyroscope is analyzed quantitatively. The three-dimensional complicated motion in the different categories is analyzed. The nonlinear differential equations in the different categories is derived and linearized by the minor variables method, and then the three-dimensional motion equations on the rotation, precession, nutation and slipping of the gyroscope in the different categories is established. Take the big gym gyroscope as the example, the influence of the force, time and position of the whip on the motion state of the gyroscope is analyzed in detail, and provides the basis for the design of the gyroscope.