The equilibrium and the stability of the Dedekind ellipsoids

Abstract

Figures or equilibrium of liquid masses with internal motions of uniform vorticity define the Dedekind sequence. It has been known for a long time that the Dedekind sequence of stationary ellipsoids is congruent to the Jacobian sequence of uniformly rotating ellipsoids. It is shown in this paper that the characteristic frequencies of oscillation of a Dedekind ellipsoid, belonging to the second harmonics, are identical with those of a Jacobi ellipsoid having the same figure; but that the points at which instability sets in by a mode of oscillation belonging to the third harmonics are different along the two sequences.