🎬stability and complexity of motion are governed by the relationship between the angular velocity and

The two rotational demos effectively illustrate a core principle of rigid body dynamics: the stability and simplicity of motion are governed by the alignment between the angular velocity ( $\omega$ ) and the body's principal axes of inertia. When the ellipsoid rotates about an arbitrary axis, the motion is complex and precessional—often visualized as a wobble— because the angular momentum ( L ) is not parallel to $\omega$, a condition that is inherently unstable without an external torque. In sharp contrast, when the rotation occurs perfectly around a principal axis, the motion is a simple, stable, pure rotation where the surface markers trace perfectly circular trails, indicating that L and $\omega$ are parallel.

Proof of the Rotational Identity | Proof and Derivationviadean on Notion