A geometric theory of rapidly spinning tops, tippe tops, and footballs

A perturbative geometric theory of rapidly spinning tops is presented and applied to gyroscopes supported against gravity at a fixed point, tippe tops with sliding friction, the motion of a well-thrown football pass, and the effect of spin-drag torques. The theory provides a conceptually simple and formally straightforward analysis of the smoothed variation of the angular momentum vector, and of the angle between it and the symmetry axis.