The problem of optimal control of the movement of a holonomic, scleronomic mechanical system of limited kinetic energy, under the effect of control that has the nature of a generalized force, of limited intensity, is discussed. The motion is observed in the phase space, so the condition of the limitation of the kinetic energy determines a closed set in that space. By using Pontryagin's maximum principle and other necessary conditions, the structure of the optimal control was determined and a sufficient number of equations and conditions were set for the solution of the problem in its final form.