Towards automatically generated variational integrators

Many fundamental physical systems have variational formulations, such
as mechanical systems in their Lagrangian formulation. Direct
discretization of the relevant variational principles leads to what
are called variational integrators. For many systems this generates
(implicit) symplectic and momentum preserving one step integration
methods.  However, such methods can be very complicated and time
consuming to implement.

 I will describe some advances in the basic theory of variational
 integrators, which allow us to automatically convert any ordinary one
 step method into a variational integrator of the same order.  I will
 also describe some work in progress towards a system which does that.