Estimates of Solutions During Motion of the Euler –Poinsot Top and Explanation of the Experiment with Dzhanibekov’s Nut

This paper presents secure upper and lower estimates for solutions to the equations of rigid body motion in the Euler case (in the absence of external torques). These estimates are expressed by simple formulae in terms of elementary functions and are used for solutions that are obtained in a neighborhood of the unstable steady rotation of the body about its middle axis of inertia. The estimates obtained are applied for a rigorous explanation of the flip-over phenomenon which arises in the experiment with Dzhanibekov’s nut.