Euler’s equations — UPSC Physics Optional IFoS 2022 Paper I

Consider the force-free motion of a symmetrical rigid body with z-axis as its axis of symmetry. Write down Euler's equations. Integrate them and obtain the solutions. On the basis of the obtained solutions show that the total angular velocity \vec{\omega} of such a rigid body is constant in magnitude and precesses about the z-axis with a constant frequency, say \Omega. Determine \Omega.