An actuator for the attitude control of a spacecraft comprises a first flywheel (1) rotated by a motor (5) and a second flywheel (2). The two flywheels (1, 2) are rotationally moveable about an axis (61) and are mechanically coupled by mechanical coupling means (4) imposing between a rate of rotation ω1 of the first flywheel (1) and a rate of rotation ω2 of the second flywheel (2) a ratio R = ω2 / ω1 which is negative on the one hand and continuously modifiable by the coupling means (4) in response to a command on the other hand so as to modify the total angular momentum of the actuator with constant total kinetic energy of the wheels. In one embodiment, the two flywheels have the same inertia and are coupled by means of a toroidal variator whose ratio R varies between -3 and -1/3. In order to store and retrieve energy at constant angular momentum, the motor (5) drives the flywheels (1, 2) in rotation and operates as a generator so as to brake said flywheels.
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