Analysis of the Rotational Motion of the Spinning Top on the Frictionless Plane

Abstract

This thesis analyzes the rotational motion of the symmetric spinning top both about a fixed pivot point and about an unfixed pivot point on a frictionless plane and compares the two models. The Euler–Lagrange equations for the spinning top are constructed from the appropriate Lagrangian functions of the two mentioned cases. From the equations, two sets of time evolution equations for the Euler angles that represent the orientation of the spinning top have been derived and solved numerically for the two cases. By using the solutions, precession and nutation of the spinning top are visualized in graphs and animated images and are compared for the two cases. The range of the nutation angle, one among the three Euler angles, between the vertical axis of the inertial frame and the spin axis of the spinning top is obtained both analytically and numerically for the two cases. Based on the range of the nutation angle, an explicit analytical method of obtaining the ranges of the three individual components of the angular velocity of the spinning top has been newly developed for the two cases. Finally, the validity of a generalized version of Euler’s law, suggested by G. H. Song especially for the case of the rotational motion of the rigid body about a moving pivot point, has been proved numerically for the two cases.