An actuator device for actuating a swivel-mounted member carried by a rotor of a propulsion engine including: at least one electricity source; an electric actuator for swiveling the swivel-mounted member; a power supply circuit connecting the electricity source to the actuator; and an inertial device connected to the power supply circuit, the inertial device configured to convert electrical energy coming from the power supply circuit into mechanical energy, to store the mechanical energy, and to convert the mechanical energy into electrical energy for the power supply circuit.