Using Quarternion to Compose Rotations (UMAP)

The purpose of this module is for students to learn the definition of the quaternions and some of its algebraic properties, as well as to calculate the result of two rotations about different axes in 3-space.

Table of Contents:

1. INTRODUCTION

2. CONTEXTS IN WHICH ROTATIONS ARE COMPOSED

3. THE QUATERNIONS

4. ADDITION AND MULTIPLICATION

5. CONJUGATION AND NORM

6. THE QUATERNIONS ARE A SKEW-FIELD

7. POLAR REPRESENTATION OF QUATERNIONS

8. DEFINITION OF THE MULTIPLICATION LINEAR OPERATOR - THE BASIC THEOREM

9. THE MULTIPLICATION OPERATOR IS REALLY A ROTATION

10. APPLICATIONS TO ROTATIONS

11. THE ORIGINAL QUESTION ANSWERED

12. HISTORICAL NOTE

13. MODEL EXAMINATION

14. ANSWERS TO EXERCISES

15. ANSWERS TO THE MODEL EXAMINATION