A Herglotz-based integrator for nonholonomic mechanical systems

TL;DR

This paper introduces a novel numerical integrator for nonholonomic mechanical systems based on the Herglotz variational principle, capable of handling both conservative and nonconservative cases, and validated through numerical experiments.

Contribution

The paper presents a new integrator that discretizes constraints and the Herglotz principle simultaneously, improving simulation accuracy for nonholonomic systems.

Findings

The integrator accurately models nonholonomic systems in simulations.

It performs better than standard methods in preserving system properties.

Validated on various numerical examples.

Abstract

We propose a numerical scheme for the time-integration of nonholonomic mechanical systems, both conservative and nonconservative. The scheme is obtained by simultaneously discretizing the constraint equations and the Herglotz variational principle. We validate the method using numerical simulations and contrast them against the results of standard methods from the literature.