Solution to the Gyroscope

Here is the link to my paper that derives the complete mathematical
solution to the gyroscope (the spinning top) in closed form.

The abstract is,
"The closed form solution is found for the fully nonlinear dynamics of
the gyroscope with a fixed point at the tip. The solution is found by
using Cardano=92s formulae to factor a cubic, in the case where all
roots are know to be real. From this, the nutation angle is solved
first in terms of Jacobi=92s elliptic integral of the first kind. A
simple change of variables then transforms the dependent variable of
the remaining equations from time to the projection of the nutation
angle onto the vertical axis. After this transformation, the
remaining equations can be integrated exactly, giving solutions
expressed in Jacobi=92s elliptic integrals of the third kind. Reduced
energy, angular momentum and moment of inertia are defined."