On the control synthesis for mechanical systems in specified motion

The paper deals with the dynamic analysis and the synthesis of control of mechanical systems in specified motion. The program requirements are treated as so-called program constraints and the control reactions ensuring the realization of the constraints are determined. In general, available control forces of the system may not project explicitly into directions orthogonal to the manifolds of particular constraints. Thus, the problem at hand is more general then the classical problem of the dynamic analysis of constrained systems and the determination of constraint reactions. It is proved (and illustrated by examples) that the program constraints can be realized by control forces which have any directions respective the constraint manifolds, and in extreme, by tangent control forces. Criteria for solvability of the problem (controllability of a system in a given program motion) are formulated, and a systematic formulation of the solution of the problem is proposed. Two illustrative examples are included.