Realizing constraints in the dynamics of systems with rolling

The possibilities of realizing constraints in the motion of systems containing kinematic pairs with small relative slips are investigated. It is shown that the limiting transition to infinite hardness of the contact forces (zero values of the slip velocities) can result in both classical non-holonomic systems and non-classical systems with primary Dirac constraints. The manifold defined by these non-classical constraints is not close to the manifold specified by the no-slip conditions in the general case. Situations in which particular constraints are realized are distinguished after examining the orders of magnitude of the terms on the right-hand and left-hand sides of the relations between the slip velocities and the generalized velocities.