Optimum oscillations suppression of the solid body at its motion round the fixed point

The technique of construction of approximately optimal controls at oscillations suppression of a solid body at its motion concerning a fixed point is developed. The technique is based on joint application of a principle of dynamic programming of Bellman and an averaging method. The considered method has appendices in dynamics of controlled motion of space vehicles in atmosphere, at stabilization of motion of the small space vehicle on a tether and in other problems, close to motion of a solid body in a classical case of Lagrange.