DYNAMIC ANALYSIS OF GYROSCOPE PRECESSION AND NUTATION BASED ON THE ANGULAR MOMENTUM THEOREM IN SPHERICAL COORDINATES

The counterintuitive phenomenon of precession and nutation of gyroscopes in the gravitational field is surprising, but qualitative explanations using Cartesian coordinate systems can only explain precession but not nutation, and cannot provide satisfactory answers for students in the general physics and mechanics stage. This paper derives the form of the angular momentum theorem in spherical coordinates and applies it to the dynamic analysis of the precession and nutation of gyroscopes. With the help of numerical simulation methods, several relationship diagrams of the gyroscope's motion quantities are given, providing students with clear dynamic images and allowing ordinary physics students to understand the complex motion of gyroscopes. This analysis method is simpler, more intuitive, and easier to understand than the Lagrangian mechanics method of theoretical mechanics.