Controlling the Amplitude of Oscillations of Mechanical Systems

An original method for searching for the optimal control of the oscillation amplitude in the vicinity of the equilibrium position of a scleronomic multidimensional mechanical system is proposed. One degree of freedom of the system is not amenable to direct control. Its movement is affected by other directly controlled degrees of freedom. Directly controlled degrees of freedom can include both positional and cyclic coordinates. The method does not contain adjoint variables in the sense of L.S. Pontryagin and does not increase the dimension of the analyzed original system of differential equations. The effectiveness of the proposed method is demonstrated on the example of a specific pendulum system.