Generalized Quaternion and Rotation in 3-space E (3-alfa,beta)

TL;DR

This paper explores the use of unit generalized quaternions for representing 3D rotations, reviewing their algebraic properties and relation to rotation matrices to enhance understanding of spatial transformations.

Contribution

It introduces the application of generalized quaternions to 3D rotations and clarifies their algebraic properties and connection to rotation matrices, expanding quaternion-based rotation methods.

Findings

Generalized quaternions effectively represent 3D rotations.

Algebraic properties of generalized quaternions are characterized.

Relation between generalized quaternions and rotation matrices is established.

Abstract

The paper explains how a unit generalized quaternion is used to represent a rotation of a vector in 3-dimensional space. We review of some algebraic properties of generalized quaternions and operations between them and then show their relation with the rotation matrix.