On the exponential stability of the permanent rotational motion of a gyrostat

This paper is devoted to the study of the problem of exponential asymptotic stability of the rotational motion of a gyrostat using servo-control moments which are applied to the internal rotors. The servo-control moments which impose the rotational motion are obtained. The stabilizing servo-control moments are obtained from the conditions to ensure exponential asymptotic stability of the desired motion. Estimations of the phase coordinations as exponential functions are presented. The method based on a choice of the structural form of the servo-control moments such that the equations of motion reduce to a system of differential equations with exponential asymptotic stability of an special solution.