Optimal Control with Two Component Physical Pendulum Oscillate

The paper concerned with analysis of oscillating motions of two component physical pendulum. Setting and solution of two optimal control problems of maximum deflection from vertical line of the first component of the pendulum are given. At the first problem the angular velocity of second component used as control function. The problem is reduced to standard form. The solution contains irregularity of control function. At the second problem the deflaction angle of second component is used as control function. It is solved by means of using of functional variation. The necessary conditions of extremum are obtained. The problem is multiextremal and nonterminated. Algorithms for solution of the problems are suggested. Numerical results are given.