  Vakonomic mechanics has been proposed as a possible description of the
dynamics of systems subject to nonholonomic constraints. The aim of the present
work is to show that for an important physical system the motion brought about
by vakonomic mechanics is completely inequivalent to the one derived from
nonholonomic mechanics, which relies on the standard method of Lagrange
multipliers in the d'Alembert-Lagrange formulation of the classical equations
of motion. For the rolling coin on an inclined plane, it is proved that no
nontrivial solution to the equations of motion of nonholonomic mechanics can be
obtained in the framework of vakonomic mechanics. This completes previous
investigations that managed to show only that, for certain mechanical systems,
some but not necessarily all nonholonomic motions are beyond the reach of
vakonomic mechanics. Furthermore, it is argued that a simple qualitative
experiment that anyone can perform at home supports the predictions of
nonholonomic mechanics.
