Walter Nadler, Hans H. Diebner and Otto E. Rössler:
Space-Discretized Verlet-Algorithm from a Variational Principle.
Z. Naturforsch. 52 a, 585-587 (1997).
A form of the Verlet-algorithm for the integration of Newton's equation of motion is derived from Hamilton's principle in discretized space and time. It allows the computation of exactly time-reversible trajectories on a digital computer, offers the possibility of systematically investigating the effects of space discretization, and provides a criterion as to when a trajectory ceases to be physical. (pdf)