Local Variational Priciples of Mechanics for Systems with Nonlinear Differential Constraints

The structure of a set of mechanical system's reactions for realization of constraints in a process of a motion is detected. The notion of virtual displacements is generalized for systems with differential nonlinear retaining constraints. The correctness of local principles of mechanics is verified for the generalized notion of virtual displacements. The generalization of Voronec's equations is received for systems under consideration.