An introduction to variational integrators

In this talk we shall introduce the basic notions of geometric integration of mechanical systems, naturally described by Lagrangian/Hamiltonian dynamics. The numerical approximation of such dynamics, respecting its underlying geometrical aspects, represents a crucial challenge in modern geometric integration. Variational integrators [MaWe2001], a class of geometric integrators that has received a lot of attention from the mathematical community in the last two decades, are a well-established example of numerical schemes that succeed in such a task, and moreover display a superior performance in some aspects than benchmark numerical integrators. We shall go over their definition and fundamental properties. Finally, we shall also introduce future challenges of variational integrators when approximating the dynamics of dissipative mechanical systems.

[MaWe2001] J.E.Marsden and M. West: “Discrete mechanics and variational integrators”, Acta Numerica 10, pp. 357-514, (2001).