Rotational Motion of a Rigid Body under Internal Dissipation
    The animation on this page depicts the rotational motion of a rigid base body that is subject to some internal energy dissipation. Possible mechanisms for energy dissipation are structural damping in flexible appendages (such as antennae) and friction between internal moving parts. Since the dissipation is due to internal forces, the overall angular momentum  remains the same.  As a result, the rotational state of the body gravitates from high kinetic energy states to low kinetic energy states on the same anugular momentum level set.

    The animation on the right shows the angular momentum ellipsoid (not the kinetic energy ellipsoid!) of the body. The principal geometrical axes of the ellipsoid (shown by white segments in all the animations) lie along the principal axes of inertia of the body, with the longest geometrical axis along the minor principal axis of inertia and the shortest along the major principal axis of inertia. The white segments in the animations thus show the instantaneous orientation of the principal axes frame of the body. The black lines depict the (nonrotating) inertial reference frame for comparison.

    The animation on the right shows the rotational motion that results when the initial angular velocity of the body is close to its minor principal axis of inertia, which is also the longest geometrical axis of the ellipsoid. Since pure spin about the minor principal axis has the greatest kinetic energy for a given angular momentum magnitude, the initial kinetic energy in our simulation is close to the maximum possible. The blue circle shows the tip of the angular velocity vector which is depicted by the blue segment. A nonrotating observer sees the angular velocity vector trace out the yellow herpolhode, while an observer rotating with the body sees the angular velocity vector trace out the red polhode. The polhode spirals onto the major principal axis, the shortest geometrical axis of the ellipsoid. As kinetic energy is dissipated, the major axis comes to rest while the ellipsoid itself ends up spinning about the major principal axis. This is because pure spin about the major axis represents the state with the least kinetic energy for a given angular momentum.

                                                         The animation appearing on this page was created with the help of Debashish Bagg.