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Robert Piziak
Department of Mathematics
Baylor University
Waco, Texas 76798-7328
piziakr@baylor.edu

Danny W. Turner
Department of Mathematics
Winthrop University
Rock Hill, SC 29733
turnerd@winthrop.edu

Hamilton's algebra of quaternions is introduced and implemented using Mathematica Version 4. The polar form of a quaternion is developed and is applied to the problem of computing the effect of a sequence of rotations on an object in three-dimensional space. Quaternion equivalents for rotations via Euler angles are illustrated.

Introduction

Real Quaternions

The Polar Form of a Quaternion

Rotations

Multiplication Is Rotation

A Graphics Animation via Quaternions

Euler Angles

A Graphics Animation via Euler Angles

References


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