Consider a thin homogeneous plate with principal moment a of inertia




Let the origins of the xi and xi systems coincide and be located at the center of mass O of the plate. At time t = 0, the plate is set rotating in a force-free manner with an angular velocity Ω about an axis inclined at an angle a from the plane of the plate and perpendicular to the x2-axis. If l1/l2 ≡ cos 2a, show that at time t the angular velocity about the x2-axis is w2(t) = Ω cos a tanh (Ω t sin a)

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4 along the principal axis x > 4 along the principal axis xg I = 1 + , along the principal axis x3