Dissipative motion of a spinning heavy symmetric top

Abstract

Dissipation is one of the important factors determining the motion of a gyroscope or heavy symmetric top in real life. In this work, for such motions, friction at the touchpoint with horizontal surface and drag are approximated with simple models, and they are considered as torque in Euler equations. Using this model, we study the motion of a gyroscope and a heavy symmetric top numerically. For the gyroscope, the effect of dissipation is studied while it is spinning without nutation and precession. For the heavy symmetric top, we consider two different types of motion, obtained experimentally in an earlier work in the literature. The numerical results show that results similar to those achieved experimentally, with the exception of the dissipative change in inclination angle, can be obtained numerically via this simple model, by utilizing Euler equations.