Optimum rotation of solid body with 1 axis of symmetry

The problem of control of motion of a solid body about its center of mass is examined, and the equations of motion are given. The formalism of quaternions is used in describing the motion. Pertinent kinematic equations are indicated and boundary conditions are set for the positions of the solid body and its angular velocity. The Pontryagin maximum principle is used. The problem can be reduced to solution of a closed system of nine differential equations. Equations are derived for minimizing rotation and a functional having the sense of expenditure of the working medium.