Mid-point embedding of Hamiltonian systems and variational integrators

TL;DR

This paper introduces a new derivation of mid-point variational integrators for Hamiltonian systems using an adapted discrete calculus, clarifying the link between discrete and continuous formulations.

Contribution

It provides a novel derivation method for variational integrators and clarifies the correspondence between discrete and continuous Hamiltonian systems.

Findings

New derivation of mid-point variational integrators

Clearer correspondence between discrete and continuous systems

Comparison with previous results by Wendlandt and Marsden

Abstract

Following the discrete embedding formalism, we give a new derivation of the mid-point variational integrators as developed by J.M. Wendlandt and J.E. Marsden by defining an adapted order two discrete differential and integral calculus. This allows us to obtain a clearer correspondence between the discrete and continuous case. We also discuss the corresponding definition of a discrete Hamiltonian system. A complete comparaison with the results of J.M. Wendlandt and J.E. Marsden is provided.