In order to analyze the relationship between nutation and precession of gyroscope with damping

equation of motion of gyro is established by static and dynamic method from dynamical model of gyroscope.Models of precession and nutation in condition of ideality and damping are deduced.It is presented that the angle on the direction of nutation includes nutation caused by gravity torque and axis precession caused by damping torque on direction of vertical axis.The swing curves of precession and nutation are produced by experiments and it is proved that damping can effectively eliminate nutation.It can provide theoretical judgment for research on nutation of gyroscope.