A counterexample showing the semi-explicit Lie-Newmark algorithm is not variational

TL;DR

This paper provides a counterexample demonstrating that the semi-explicit Lie-Newmark algorithm is not variational, indicating its limitations for long-term simulations of rigid body systems.

Contribution

It introduces a specific counterexample that disproves the variational property of the Lie-Newmark method, highlighting its potential drawbacks.

Findings

Lie-Newmark algorithm is not variational

Counterexample involves a rigid body in a static potential

Method is less suitable for long-time simulations

Abstract

This paper presents a counterexample to the conjecture that the semi-explicit Lie-Newmark algorithm is variational. As a consequence the Lie-Newmark method is not well-suited for long-time simulation of rigid body-type mechanical systems. The counterexample consists of a single rigid body in a static potential field, and can serve as a test of the variational nature of other rigid-body integrators.