Hamel's Formalism and Variational Integrators on a Sphere

TL;DR

This paper explores Hamel's formalism combined with variational integrators to develop structure-preserving numerical methods for mechanical systems on spheres, avoiding coordinate singularities and differential-algebraic equations.

Contribution

It introduces a novel approach using minimal redundancy in coordinates to improve integration of systems on spheres, bypassing common singularities and algebraic constraints.

Findings

Developed a coordinate system that avoids singularities on the sphere

Proposed a variational integrator based on Hamel's formalism

Achieved structure-preserving numerical integration without DAE complexity

Abstract

This paper discusses Hamel's formalism and its applications to structure-preserving integration of mechanical systems. It utilizes redundant coordinates in order to eliminate multiple charts on the configuration space as well as nonphysical artificial singularities induced by local coordinates, while keeping the minimal possible degree of redundancy and avoiding integration of differential-algebraic equations.