On realization of program constraints: Part I - Theory

The problem of realization of program constraints is considered. The classical theory approach based on replacing the constriant reactions by adequate control forces has been generalized to the case when the control forces are not collinear with program constraint vectors or, in the extreme, when the control forces do not project in these directions at all (control forces are tangent to constraint manifolds). A classification of possible ways of program constraint realization is proposed and a general solution of the problem is presented.