  Problems involving rolling without slipping or no sideways skidding, to name
a few, introduce velocity-dependent constraints that can be efficiently treated
by the method of Lagrange multipliers in the Lagrangian formulation of the
classical equations of motion. In doing so one finds, as a bonus, the
constraint forces, which must be independent of the solution of the equations
of motion, and can only depend on the generalized coordinates and velocities,
as well as time. In this paper we establish the conditions the Lagrangian
should obey that guarantee that the constraint forces can be obtained
consistently.
