The attitude dynamics of a nanosatellite (NS) with one movable unit changing its angular position relative to a main body of the nanosatellite is considered. This relative movability of the unit can be implemented with the help of flexible rods of variable length connecting the unit with the main body. Change of the relative position of the movable unit shifts the center of mass of the entire mechanical system. The NS has a single jet engine rigidly mounted into the NS main body. The shift of the mass center creates an arm of the jet-engine thrust and a corresponding control torque. Schemes to control the attitude dynamics of the satellite using the movability of its unit are developed, using both the torque from the engine and inertia change.