A rigid body has an axis of symmetry, which we designate as axis 1. The principal moment of inertia about this axis is \(I_{1}\), while the principal moments of inertia about the remaining two principal axes are \(I_{2}=I_{3} \equiv I_{0} eq I_{1}\). (a) Write the Euler equations of rotational dynamics in terms of \(I_{1}, I_{0}\), and the three angular velocities \(\omega_{1}, \omega_{2}, \omega_{3}\). (b) Show that \(\omega_{1}\) is constant. (c) Find a second-order linear differential equation for \(\omega_{2}\) and another for \(\omega_{3}\). (d) Does either the magnitude or direction of this precession depend upon whether the rigid body is prolate (like an American football or rifle bullet) or oblate (like a saucer or frisbee)? (e) Prove that the symmetry axis of the rigid body is coplanar with the angular velocity vector \(\boldsymbol{\omega}\) and with the angular momentum vector \(\mathbf{L}\).