Is Symplectic-Energy-Momentum Integration Well-Posed?
arXiv:math-ph/0608016
Abstract
We provide new existence and uniqueness results for the discrete-time Hamilton (DTH) equations of a symplectic-energy-momentum (SEM) integrator. In particular, we identify points in extended-phase space where the DTH equations of SEM integration have no solution for arbitrarily small time steps. We use the nonlinear pendulum to illustrate the main ideas.
24 pages, see http://www.rose-hulman.edu/~shibberu/DTH_Dynamics/DTH_Dynamics.htm