Is it allowed, in the context of the Lagrange multiplier formalism, to assume that nonholonomic constraints are already in effect while setting up Lagrange's function? This procedure, although successfully applied in a recent book to the problem of the rolling penny, is not valid in general, as we show by means of a counterexample. In many cases the use of nonholonomic constraints in the process of construction of the Lagrangian is allowed, but the correct equations of motion are Voronec's equations.
