# 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.

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