where x , y , z are Cartesian coordinates on axes x ^ ^ , y ^ ^ , z ^ ^ aligned respectively with the a , b , c axes of the ellipsoid. Here ζ ζ is the vorticity, which is uniform throughout the spheroid ( ∇ ∇ × × u = ζ ζ z ^ ^ ). The angular velocity Ω Ω of the Jacobi ellipsoid and vorticity of the corresponding Dedekind ellipsoid are related by