Optimal control of the rotational motion of a rigid body using moving masses

Abstract

The non-linear equations of motion of a rigid body affected by white Gaussian noises are used to study the stabilization of the rotational motion with the help of internal moving masses. The control laws ensuring the tendency of the stochastic motion to the unperturbed motion and the programmed motion are determined as non-linear functions of the variables describe the stochastic and programmed motions. The programmed control law ensures the asymptotic stability with probability is obtained. An estimation of the angular velocity of the body tending to the programmed angular velocity is found.