Particular Extremals in the Optimal Control Problems of the Reorientation of an Asymmetric Rotating Body

Abstract

The optimal control problem regarding the reorientation of an asymmetric rigid body has been investigated. The integral-quadratic functional consistent with the inertial symmetry of the body, which characterizes the total energy consumption, has been chosen as the criterion. Control is considered to be the main moment of applied external forces. An explicit description of a family of extremals for an arbitrary asymmetric rigid body has been obtained. The idea of constructing such extremals is based on the study of spatio-temporal deformations for solutions of Euler differential equations of a rigid body’s free rotation.