Nonholonomic Newmark method

TL;DR

This paper generalizes Newmark methods for nonholonomic systems using the exponential map, demonstrating that composed methods can maintain good energy behavior even when structure is lost.

Contribution

It introduces a nonholonomic exponential map-based generalization of Newmark methods and shows composition improves energy behavior in challenging cases.

Findings

Composition of two Newmark methods preserves energy behavior.

Numerical examples demonstrate effectiveness despite structure loss.

Generalization extends applicability to nonholonomic systems.

Abstract

Using the nonholonomic exponential map, we generalize the well-known family of Newmark methods for nonholonomic systems. We give numerical examples including a test problem where the structure of reversible integrability responsible for good energy behaviour as described in [16] is lost. We observe that the composition of two Newmark methods is able to produce good energy behaviour on this test problem.