Optimal behavior control of an initial-boundary problem solution modelling rotation of a solid body with the flexible rod

An initial-boundary problem modelling the rotation of discrete-continuum mechanical system, which consists from a solid and the rigidly connected flexible rod. To solve the problem we determine a solution notion, prove its existence, uniqueness, and continuous dependence from start conditions and parameters of the boundary task. Are resolved tasks of solution rotation from the start phase state to the finish one at a specified time moment and with the controller function norm minimum in the $L_\infty (0,T)$ space and time control problem with a limited norm of controller function in the specified space. Maximum principe was formulated, and an algorithm of optimal control modelling is proposed. The moments problem is used as an investigation method