We find the extrema of the kinetic energy given by Eq.(2) under the condition that the magnitude of the angular velocity vector is constant:
We do not consider the case ...... and I=0 because T(w) is then constant and does not depend on the direction of the rotational axis. Another simple case is ....... and ...... where the solution for minima of the kinetic energy is clearly ...... and ....: the axis of rotation lies along the y-axis. In the following discussion, we will assume that .....
The extremal points of T(w) can be found from a set of stationary points determined by ........... Setting the derivative of Eq.4 to zero gives