On the stability of a class of precessions

The rotational motion of a rigid body around its axis of symmetry is examined under conditions corresponding to helicoidal precession. A class of helicoidal precessions is defined, and the stability of such precession is analyzed for sudden perturbations by using concepts of stability in the sense of Liapunov and in the sense of Poincare. It is shown that all members of this class of precessions are unstable in the sense of Liapunov; stability in the sense of Poincare (orbital stability) is governed by the value of the limit of pitch distance at infinity.