The investigation of damping of the spacecraft’s angular rates in the off-optimum situation

The off-optimum situation on the spacecraft, equipped with reaction wheels, is the lack of measurements of one component of the angular rate of the spacecraft relative to one of its body axes. We investigate the full-time algorithm’s operation in the damping of the spacecraft’s angular rates. We show that this damping is not possible for all initial conditions of motion. In general case, it is realized one of two possible final modes, described by the stable stationary solutions of the equations of motion. With using of numerical calculations, we have obtained the estimates of the domains of attraction of stationary solutions. We propose a simple way to bring the initial conditions for the spacecraft’s damping mode out from the domain of attraction of undesirable solutions. We reconstruct some implementations of this mode, which were took place. The reconstruction was performed by approximation of telemetry data of the components of the angular rates and the total angular momentum of the reaction wheels by equations of rotational motion of the spacecraft.