On optimal stabilization of part of variables of rotary movement of a rigid body with one fixed point in the case of Sophia Kovalevskaya

An optimal stabilization problem for part of variables of rotary movement of a rigid body with one fixed point in Sophia Kovalevskaya's case is discussed in this work. The differential equations of motion of the system are given and it is shown that the system may rotate around $Ox$ with constant angular velocity. Accepting this motion as an unexcited motion, the differential equations of the corresponding excited motion were drawn up. Then the system was linearized and a control action was introduced along one of the generalized coordinates. The optimal stabilization problem for part of the variables was stated and solved. The graphs of optimal trajectories and optimal control were constructed and shown.