Time-Optimal Rotation of a Body by Displacement of a Mass Point

Abstract

The problem of time-optimal rotation of a rigid body in the two-dimensional case by the use of mass forming a closed system with the body has been considered. For the general case, two scalar equations for two unknowns have been obtained. When the finite position of the mass is not specified, the problem is reduced to solving a single scalar equation the root of which always exists and is unique for any boundary conditions on a known segment. The relations for the optimal control, the trajectory of the mass motion, and the Bellman function are expressed in terms of elliptic integrals. The same formulas can also be used in the case when only the distance between the mass and the coordinate origin is specified at a finite instant of time.