Locally Optimal Laws of Control of a Spacecraft Motion with an Electrodynamic Engine at Circumterrestrial Orbits

The motion of a spacecraft under the action of Ampére force is investigated. This force arises as a result of the interaction of the current in a rigid rod, at whose ends the devices which close the electric circuit through the circumterrestrial plasma are located, with the magnetic field of the Earth. The locally optimal laws of control by this rod orientation are found, when one of the elements of the orbit gains the maximum increment under the action of this engine. Numerical estimates of the gained increments are obtained, and it is demonstrated that this engine is a promising tool for the execution of light spacecraft maneuvers at low circumterrestrial orbits.