DYNAMICS OF CLASSICAL-SYSTEMS BASED ON THE PRINCIPLE OF STATIONARY ACTION

Dynamics of classical systems often involve finding a path of evolution of the system between chosen initial and final configurations such as reactant and product states. We develop a method for calculating the dynamics of such classical systems posed as boundary value (configurations) problems. This method is based on recasting the principle of stationary action into a computationally tractable form which can be applied to a wide variety of boundary problems. We demonstrate that a path of minimum action does not always exist except for a short enough path. However, saddle points of the action can reveal interesting dynamical pathways. We give examples from particle mechanics and applications to reaction mechanisms for the H + H2 → H2 + H reaction. © 1990 American Institute of Physics.