Consider the effects of the inertia of the gimbals in a balanced free gyroscope. Let A, B, and C denote the (principal) moments of inertia of the inner gimbal about the x y z axes, where y is the line of nodes and z is the spin axis of the rotor. Also, let A denote the moment of inertia of the outer gimbal about the precession axis. Derive the equations of motion for the gyroscope in this case.