ON THE MOTIONS OF A RIGID BODY CONTAINING TWO-DEGREE-OF-FREEDOM CONTROL MOMENT GYROS WITH DISSIPATION IN GIMBAL AXES

摘要

We consider a system that consists of a supporting rigid body and two-degree-of-freedom gyros and is not a gyrostat in general. The equations of motion of the system under the action of arbitrary forces are derived. The case in which external couples are absent and only dissipative and potential torques act in the gimbal axes is considered. We show that the limit motions of the system are equilibrium motions in which the gyro gimbals do not move relative to the support. Differential equations for equilibrium motions and algebraic equations for steady motions are obtained. We find an auxiliary function V (the total energy calculated for "frozen" rotors) that does not increase along motions of the system and prove a theorem on the correspondence between steady motions and stationary points of V on the manifold determined by the angular momentum integral of the system. We discuss a method for stability analysis of steady motions in which V is used as a Lyapunov function. The results are generalized to the problem on the motion of a system of rigid bodies connected by hinged joints.