Lagrange multipliers for constraints

Summary

In mechanics, Lagrange multipliers let one write the equations of motion of a constrained system in redundant coordinates, without first solving the constraints. Each holonomic constraint adds one unknown function of time, its multiplier, to the Lagrange equations. The multipliers measure the forces that the constraints exert, such as the tension in a pendulum rod. This is the dynamical version of the method of Lagrange multipliers for constrained extrema. See the definition.