# Contact variational integrators

## TL;DR

This paper introduces geometric numerical integrators for contact flows based on a discretized variational principle, demonstrating their properties and comparing their performance to symplectic integrators using a damped harmonic oscillator example.

## Contribution

It develops contact variational integrators, proving they are contact transformations and establishing their backward error analysis, extending variational methods to contact geometry.

## Key findings

- The integrators are contact transformations.
- They can be derived from a variational principle.
- Performance comparison shows advantages over symplectic integrators.

## 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.