The device shown is a gyropendulum, which has been used in some applications to locate the vertical direction. The spin rate φ? is held constant by a servomotor. Let m be the mass, and let I and I be the centroidal principal moments of inertia of the flywheel parallel and transverse to the spin axis; ignore the inertia of the gimbals. Evaluate the nutation response θ (t) and the precessional response ψ (t) of the flywheel to a disturbance that causes it to rotate by very small angles away from the vertical reference position, at which θ = π/2. Compare the frequency of these responses with that of a simple pendulum, and use that result to discuss an advantage of the gyropendulum.
