The elements of a reaction-wheel attitude-control system for a spacecraft are shown in t...

The elements of a reaction-wheel attitude-control system for a spacecraft are shown in the figure. Point G is the center of mass for the system of the spacecraft and wheels, and x, y, z are principal axes for the system. Each wheel has a mass m and a moment of inertia I about its own axis and spins with a relative angular velocity p in the direction indicated. The center of each wheel, which may be treated as a thin disk, is a distance b from G. If the spacecraft has angular velocity components Ω_x, Ω_y, and Ω_z, determine the angular momentum H_G of the three wheels as a unit.