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For a fixed point a distance $a$ from the centre of mass and inclination measured from the upward vertical,The spin and precession angles are cyclic.

This is the Lagrangian of a Lagrange top, one of the Lagrange, Euler, and Kovalevskaya tops.

The Lagrange, Euler, and Kovalevskaya tops are three integrable cases of fixed-point rigid body dynamics. The Euler top has no external torque; the Lagrange top has axial symmetry and its center of mass on the symmetry axis; the Kovalevskaya top has two equal principal moments twice the third and its center of mass in the corresponding principal plane.