A Computational Approach for Variational Integration of Attitude Dynamics on SO(3)

TL;DR

This paper introduces a computational method for simulating rigid body attitude dynamics on SO(3) using variational integrators that preserve geometric structure, along with a Newton-Raphson solver for implicit equations.

Contribution

It develops a variational integrator framework on SO(3) and a Newton-Raphson algorithm for implicit equations, enhancing simulation accuracy and structure preservation.

Findings

Preserves symplectic structure during simulation

Provides an effective Newton-Raphson solver for SO(3)

Improves accuracy of rotational dynamics simulation

Abstract

In this article, a brief description of Discrete Mechanics and Variational Integrators which preserve the symplectic structure of the flow will be provided and a Newton-Raphson algorithm that can be used to solve implicit equations on the SO(3) manifold will be developed. These techniques will be used to simulate the rotational dynamics of a rigid body evolving on the Lie Group SO(3).