Feedback controlled satellite angular momentum: on the analytic solution of the angular velocity

A direct analytic solution of the angular velocities is given for regulating the angular momentum of spacecraft using reaction jets only. The main objective is to show how to get the analytic solution, when the flywheels are at rest, in a relatively simple manner. The analytic solution may be written down in terms of some characteristic values and characteristic vectors. Those values and vectors satisfy an algebraic nonlinear equation