The free precession of a rotating rigid body is a classic application of Euler's equations. Since the precession is free, there is no torque, and the angular momentum is constant in the space frame. In the body frame, however, the body axes

,

,

(indicated by the red, green, and blue spheres) are fixed, and the angular momentum

and space axes

(indicated by the red, green, and blue arrows) will change with time. For an axisymmetric ellipsoid, the angular velocity

and the angular momentum

precess about the symmetry axis

. This precession can be visualized by the rotation of a space cone (centered about

) around the body cone (centered about

), with the angular velocity

at their point of contact. This Demonstration shows the free precession as a function of time in both the body and space frames. The body's height and radius

* *can be varied, as can the initial angular velocity

.