Tippe top paradox in relativity

If a tippe top is held by its stem and spun fast on a table, it eventually tips over and stands spinning on its stem. For this to happen, the ratios of its principal moments of inertia should fall in a certain regime. Let such a top be observed from a rocket frame in which the top and the table move with a relativistic velocity. The cross-section of the top now appears elliptical due to the length contraction along the line of motion. For a fast enough rocket frame, it is possible that the ratios of the principal moments of inertia go out of the regime required for the top to tip over. However, this is paradoxical. A top that tips over in one frame should tip over in all frames. The paradox is resolved by applying the Lorentz transformation formulae to the equation of motion of the particles of the top, and going over to the spinning coordinates. All the relativistic effects such as the length contraction, time dilation, velocity addition and the lack of synchronization of clocks make their appearance. The orbits of the particles are studied analytically as well as by computer simulation. The movies on the monitor screen reveal the picturesque motion of the particles of the spinning top in the rocket frame, and show in detail how the notion of a rigid body fails in relativistic mechanics. The source code for the computer simulation is included in the appendix.