On the motion of mechanical systems in force fields, as motion in their absence when connections are applied

The possibility of reversibility of the principle of release from connections, widely used in solving problems of mechanics, is studied. The opposite position is formulated, according to which the movement of the system will not change if the forces acting on it are ignored and connections are imposed, the reactions of which provide the initial movement. In this case, the studied mechanical system is obtained from another, with a large number of degrees of freedom, on which both holonomic ideal connections and nonholonomic ones are superimposed, and movement occurs in the absence of active active forces. The main task is to determine the equations of relations in an expanded space of configurations that uniquely generate given force fields in the original space.