A Family of Extremal Angular Velocity Vector Functions with a Constant Absolute Value in the Problem of Optimal Reorientation of a Spherically Symmetric Body with Minimal Energy Consumption

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.