Stochastic dynamics of constrained systems

We consider the stochastic dynamics of constrained systems. It is shown that by expressing the Lagrange multipliers in terms of quantities that are local in time, exact and potentially useful dynamic equations of the Langevin, Fokker-Planck and Smoluchowskii equations are obtained. The equations do not require the introduction of coordinates on the manifold to which the system is restricted but have a symmetric form and are described in terms of the coordinates of the embedding space.