where are Cartesian coordinates on axes aligned respectively with the axes of the ellipsoid. Here is the vorticity, which is uniform throughout the spheroid (). The angular velocity of the Jacobi ellipsoid and vorticity of the corresponding Dedekind ellipsoid are related by

That is, each particle of the fluid of the Dedekind ellipsoid describes a similar elliptical circuit in the same period in which the Jacobi spheroid