MacCullagh ellipsoid

The MacCullagh ellipsoid is defined by the equation:


 * $$\frac{x^2}{A} + \frac{y^2}{B} + \frac{z^2}{C} = 2 E,$$

where $$E$$ is the energy and $$x,y,z$$ are the components of the angular momentum, given in body's principal reference frame, with corresponding principal moments of inertia $$A,B,C$$. The construction of such ellipsoid was conceived by James MacCullagh.