the alignment with the intermediate axis is not perfect then will eventually move off this point along one of the four tracks that depart from this point, and head to the opposite point. This corresponds to moving to its antipode on the Poinsot ellipsoid. See video at right and Tennis racket theorem. This construction differs from Poinsot's construction because it considers the angular momentum vector rather than the angular velocity vector . It appears to have been developed by Jacques Philippe Marie Binet. Special case In the general case of rotation of an unsymmetric body, which has different values of the moment of inertia about the three principal axes, the rotational motion can be quite complex unless the body is rotating around a principal axis. As described in the tennis racket theorem, rotation of an object around its first or third principal axis is stable, while rotation around its second principal axis (or intermediate axis) is not. The motion is simplified in the case of an axisymmetric body, in which the moment of inertia is the same about two of the principal axes. These cases include rotation of a prolate spheroid (the shape of an American football), or rotation of an oblate spheroid (the shape of a flattened sphere). In this case, the angular velocity describes a cone, and the polhode is a circle. This analysis is applicable, for example, to the axial precession of the rotation of a planet (the case of an oblate spheroid.) Applications One of the applications of Poinsot's construction is in visualizing the rotation of a spacecraft in orbit. See also Polhode Precession Principal axes Rigid body dynamics Moment of inertia Tait–Bryan rotations Euler angles MacCullagh ellipsoid Rattleback References Sources Poinsot (1834) Theorie Nouvelle de la Rotation des Corps, Bachelier, Paris. Landau LD and Lifshitz EM (1976) Mechanics, 3rd. ed., Pergamon Press. (hardcover) and (softcover). Goldstein H. (1980) Classical Mechanics, 2nd. ed., Addison-Wesley. Symon KR. (1971) Mechanics, 3rd. ed., Addison-Wesley. External links Poinsot construction in stereo 3D simulation - online and free. Rigid bodies