Contact variational integrators
Numerical Analysis
2019-11-04 v4 Numerical Analysis
Mathematical Physics
math.MP
Abstract
We present geometric numerical integrators for contact flows that stem from a discretization of Herglotz' variational principle. First we show that the resulting discrete map is a contact transformation and that any contact map can be derived from a variational principle. Then we discuss the backward error analysis of our variational integrators, including the construction of a modified Lagrangian. Throughout the paper we use the damped harmonic oscillator as a benchmark example to compare our integrators to their symplectic analogues.
Keywords
Cite
@article{arxiv.1902.00436,
title = {Contact variational integrators},
author = {Mats Vermeeren and Alessandro Bravetti and Marcello Seri},
journal= {arXiv preprint arXiv:1902.00436},
year = {2019}
}