陀螺进动中的“角动量不守恒”问题

THE EXPLAINATION OF “NONCONSERVATION OF ANGULAR MOMENTUM” IN GYROSCOPIC PRECESSION

一些力学教科书中对回转效应的讲解就是直接利用重力力矩导致陀螺角动量变化得到均匀进动角速度,但是这会导致竖直方向出现进动角动量而无法解释的问题,即看似角动量不守恒。本文从基本的力学原理出发,分析了陀螺水平释放后从开始到稳定过程中的进动和章动,并对结果进行了数值模拟,证明忽略进动阻尼时稳定进动角动量与陀螺下倾导致的自转角动量竖直分量大小相等、方向相反,保证了系统竖直方向角动量恒为零。

During the teaching practice,We found it only shows how to get the stable angular velocity of precession with moment of gravity resulting in the change of rotation momentum about gyroscopic effect in some text books.It will make students get confused with the origin of angular momentum of precession,and seems like a nonconservation of angular momentum.In this paper,based on the basic principles of mechanics,the precession and nutation of the gyroscope from the beginning to the stabilization process are analyzed,and the results are numerically simulated.It is proved that the stable angular momentum of procession and the vertical component of the rotation momentum of the gyroscope are equal in numerical value,but with opposite directions,which ensure the total angular momentum in the vertical direction of the system identically equals to zero.