Optimal control of damping rotation of a rigid body using fly wheels with friction

In this paper we study the problem of optimal control of a rigid body damping rotation with the help of three fly wheels taking into account the wheel friction. Given a quadratic performance index we seek reaction wheels that minimize it and asymptotically stabilize a rigid body rotation around the Euler axis. The damping rates of the angular velocity of the body are obtained. Many of special cases are obtained from the deduced results. Numerical simulation of the obtained results is presented.