Earlier, a method was developed for modeling the dynamics of systems with geometric constraints using the analytical mechanics of systems with redundant coordinates and the theory of nonlinear stability. In the present paper, the previously obtained results are applied to the construction of a mathematical model and to the solution of the stabilization problem of steady motion for the simplest manipulator with one positional, one cyclic and one dependent coordinate. The analysis is carried out taking into account the dynamics of the drives. For steady motion, the solvability of the problem of determining the stabilizing control (additional voltage on the executive motors) by solving the linearly quadratic problem by the method of NN Krasovskii is proved. Asymptotic stability in a complete nonlinear closed system follows from the previously proved theorem on asymptotic stability in the presence of zero roots of the characteristic equation corresponding to redundant coordinates. However, for the manipulator design under consideration, stable operation modes can be distinguished even with constant voltage on the drive motors. These voltages play the role of program controls, ensuring the implementation of this mode of operation. The results of numerical simulation are presented.