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Real Quaternions and Rotations

Robert Piziak
Organization: Baylor University
Department: Department of Mathematics
Danny Turner
Organization: Winthrop University
Department: Department of Mathematics
Journal / Anthology

The Mathematica Journal
Year: 2002
Volume: 8
Issue: 3
Page range: 458-472

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

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.

*Mathematics > Algebra > Field and Ring Theory