Abstract
The problem of optimal control of reorientation of an absolutely rigid spherically symmetric body is investigated. An integral-quadratic functional characterizing the total energy consumption was chosen as a criterion for the effectiveness of maneuver. Main moment of applied external forces serves as control. In this problem, for the first time, a family of analytic extremal trajectories is obtained, which are uniquely determined in accordance with the requirement that the absolute value of the angular velocity vector function be constant in time. Illustrative examples are provided.
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