陀螺仪进动与章动运动分析

Movement analysis of precession and nutation of gyroscope

为了分析阻尼条件下陀螺仪章动与进动关系,从陀螺仪动力学模型出发,利用动静法建立运动方程,推导出理想条件下和阻尼条件下的进动与章动模型,指出章动方向上角度的变化中包含重力矩引起的章动和铅垂轴方向阻尼力矩引起的转子轴进动2个方面的影响,并通过实验得到进动和章动摆动曲线,同时证明阻尼能有效消除章动,为以后研究陀螺仪章动提供理论依据。

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