A new principle and linked schemes of reaction/momentum wheels unloading are proposed and constructed. This principle is based on the instantaneous restructuring and changing the mechanical system itself, when additional internal degrees of freedom become available. These releasing additional degrees of freedom correspond to additional rotors, which take “after unfreezing” their own opportunity to rotate. At the connection of additional “unfrozen” rotors to the main wheels by gear type, these rotors become involved in the rotation with opposite direction relatively to the main wheels rotation, and it instantaneously provides nulling the relative angular momentum. Then electric motors of additional rotors and wheels can start the process of the rotational energy recovery, which decelerates and unloads angular velocities of all rotors and wheels. The proposed principle of releasing additional degrees of freedom and reconfiguring internal mechanical multi-rotor subsystem allow to immediately change values and directions of the relative angular momentum. This changeable multi-rotor subsystem represents the multifunctional attitude control system, which can be figuratively called as a “gearbox”. As a part of the gearbox a special mechanical device is proposed, which represents a “gravitational damper” to unloading the total absolute angular momentum of spacecraft with the help of external gravitational torques.