A rotating free rigid body can be analyzed with the so called Poinsot construction:
- Conservation of moment of inertia and energy give two ellipsoids, intersecting in another ellipsoid
- Angular momentum moves in a precession but nonetheless is at every moment normal to the ellipsoid
- Thus, from the point of view of the plane normal to angular momentum, the ellipsoid rolls without slipping along a curve called herpoloid
Or something like that.
Is it possible to analyze the motion of this abstract rolling ellipsoid, regarded as a physical system?
This article generalizes the Poinsot construction, so it may be useful.