Variational integrator

Summary

A variational integrator is a numerical method for Lagrangian mechanics obtained by discretising Hamilton's principle of stationary action instead of the equations of motion. One approximates the action over a single time step by a discrete Lagrangian. Asking the sum of these to be stationary gives the discrete Euler–Lagrange equations. These methods are automatically symplectic and keep the momenta that come from symmetries, by a discrete Noether theorem, so they are geometric integrators.