Optimization of mechanical systems oscillations

The problem of control of oscillations in the vicinity of the equilibrium position of a scleronomic mechanical system with several degrees of freedom is solved. One degree of freedom is not controllable directly, and the rest are controlled by servos. An original method is proposed for finding the optimal control of amplitude of oscillations of the uncontrolled degree of freedom by the choice of control of other degrees of freedom. The set of controlled coordinates can include both positional and cyclic coordinates. Compared to Pontryagin’s maximum principle, the proposed method does not contain conjugate variables and significantly reduces the dimension of the analyzed system of differential equations. The effectiveness of the proposed method is demonstrated by the example of a specific pendulum system.