Hamilton's theory of turns revisited

TL;DR

This paper introduces a simplified approach to Hamilton's theory of turns for SO(3) and SU(2), making their properties and composition law more transparent by using binary rotations instead of mirror reflections.

Contribution

It presents a new method based on binary rotations that simplifies understanding of Hamilton's turns for SO(3) and SU(2).

Findings

Composition law becomes nearly trivial and immediately evident.

Entire construction can be based on binary rotations.

Properties of the groups are clarified through this approach.

Abstract

We present a new approach to Hamilton's theory of turns for the groups SO(3) and SU(2) which renders their properties, in particular their composition law, nearly trivial and immediately evident upon inspection. We show that the entire construction can be based on binary rotations rather than mirror reflections.