The problem of the optimal turn of a spacecraft as a rigid body with arbitrary dynamic configuration under arbitrary boundary conditions on the attitude and the angular velocity of a spacecraft in the quaternion statement is considered. The functional that combines the time and and the integral value of the modulus of the control vector required for turning the spacecraft is used as the optimality criterion. The investigation of a special control mode of a spacecraft and their application in the particular case of spherical symmetry of a spacecraft are presented. Confirming numerical examples are given.
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