  The computation of free energy differences through an exponential weighting
of out of equilibrium paths (known as the Jarzynski equality) is often used for
transitions between states described by an external parameter $\lambda$ in the
Hamiltonian. We present here an extension to transitions between states defined
by different values of some reaction coordinate, using a projected Brownian
dynamics. In contrast with other approaches, we use a projection rather than a
constraining potential to let the constraints associated with the reaction
coordinate evolve. We show how to use the Lagrange multipliers associated with
these constraints to compute the work associated with a given trajectory.
Appropriate discretizations are proposed. Some numerical results demonstrate
the applicability of the method for the computation of free energy difference
profiles.
