Quaternions and dynamics

TL;DR

This paper provides a clear introduction to quaternions and demonstrates their practical application in modeling complex rigid body dynamics, including satellite systems, highlighting their advantages over Euler angles.

Contribution

It offers a comprehensive, self-contained explanation of quaternions and their use in detailed dynamics modeling, including complex systems like satellites with inertial wheels.

Findings

Quaternions simplify the representation of complex rigid body dynamics.

The paper details the modeling of satellite systems using quaternions.

Quaternions enable manual derivation of complex dynamics equations.

Abstract

We give a simple and self contained introduction to quaternions and their practical usage in dynamics. The rigid body dynamics are presented in full details. In the appendix, some more exotic relations are given that allow to write more complex models, for instance, the one of a satellite with inertial wheels and expressed in a non-inertial reference frame. As it is well known, one nice advantage of quaternions over Euler angles, beside the usual arguments, is that it allows to write down quite complex dynamics completely by hand.