Stability of the motion of a rotating axial symmetrical solid body in a fluid

Abstract

The stability criterion of the motion of an axial symmetrical solid body rotating about its axis of revolution and moving in the direction perpendicular to its axis of rotation is obtained. The major controlling factors which stabilize a rotating top in a fluid are examined. For a flat circular top (A < B) the stabilizing effect of rotation appears less effective in the case of the rotating top translating in the direction perpendicular to the axis of rotation than parallel to the axis of rotation; the translation velocity destabilizes the rotating top in the former case but stabilizes it in the latter case.