Winding number formula for Maslov indices

A formula for the Maslov index of closed curves on Lagrangian manifolds is derived. The index is expressed as the number of times the plane tangent to the curve winds around it. Applications include unstable periodic orbits, in which case the Lagrangian manifolds are the stable or unstable manifolds of the orbits, and cycles on the invariant tori of integrable systems, in which case the manifolds are the tori themselves.