A Variational Principle for Nonholonomic Systems

The equations of motion for a Lagrangian system with velocity-dependent constraints, which cannot be obtained from the variational principle of Lagrange, are shown to follow from a different variational procedure in which the comparison paths do not satisfy the constraint conditions. The new variational problem reduces to the Lagrange problem when the constraints are holonomic. In presenting the variational problem a new approach to Lagrange multipliers is introduced.