The integration of the differential equations of motion of the symmetric top, described by the Euler
angles as coordinates, is revisited using Jacobi’s elliptic functions for the nutation angle and
Jacobi’s theta functions for the rotation ψ and precession ϕ angles. The Hamiltonian function is
first modified, making it symmetric with three equal moments of inertia, to discover the action of
the different moment of inertia just by adding only a constant angular velocity around the symmetry
axis of the top. Simultaneously, it becomes symmetric with respect to the action of rotation and
precession on nutation, since interchange of the conjugated momenta of those angles does not modify
the nutation, which is equivalent to the periodic motion of a particle in a cubic potential well.
The differential equations for the angles ϕ and ψ appear with symmetry that is simplified when
expressed in terms of the sum and difference of these angles. This approach coinc…