A space-time geodesic approach for phase fitted variational integrators

The use of space-time geodesic approach of classical mechanics is investigated, in order to derive time adaptive high order phase fitted variational integrators. The proposed technique is employed for systems of which the Lagrangian is of separable form. To this end, first the unfolding of the standard Euler-Lagrange system to its space-time manifold is presented and then it is rewritten as a geodesic problem with zero potential energy. Preliminary simulation results (without optimizing the choice of step sizing) show that one can use the spacetime geodesic formulation to generate an adaptive scheme that still preserves some underlying geometric structure.