Numerical Evolution from the Hamiltonian

We propose a numerical method for approximate calculations of the time evolution of point particle systems given only the system's Hamiltonian function and initial conditions. The method both generates and solves the equations of motion numerically. For demonstration purposes, a working implementation written in Python is described and applied to standard problems. The method may have some pedagogical merits but the numerical effort of generating the equations of motion makes it unsuitable for actual numerical solution of "real" problems with any but just a few degrees of freedom.