Rotation Sequences and the Theory of Vectors and Coordinates

This book applies rotation theory to problems involving vectors and coordinates, through easily visualised procedures and smart mathematics.

Don Koks (Author)

9781009516754, Cambridge University Press

Hardback, published 24 April 2025

566 pages
24.4 x 17 x 3.2 cm, 1.211 kg

This book applies rotation theory to problems involving vectors and coordinates, with an approach that combines easily visualised procedures with smart mathematics. It constructs rotation theory from the ground up, building from basic geometry through to the motion and attitude equations of rockets, and the tensor analysis of relativity. The author replaces complicated pictures of superimposed axes with a simple and intuitive procedure of rotating a model aircraft, to create rotation sequences that are easily turned into mathematics. He combines the best of the 'active' and 'passive' approaches to rotation into a single coherent theory, and discusses many potential traps for newcomers. This volume will be useful to astronomers and engineers sighting planets and satellites, computer scientists creating graphics for movies, and aerospace engineers designing aircraft; also to physicists and mathematicians who study its abstract aspects.

1. Setting the scene
2. Trigonometry, the foundation of coordinate theory
3. The vector dot and cross products
4. Vector preliminaries, and constructing a basis
5. Converting vector coordinates across bases
6. Vector rotation in two and three dimensions
7. Rotation sequences and the fundamental theorem
8. Coordinate systems for Earth, and more rotation sequences
9. The role of quaternions in rotation theory
10. Time dependence of vehicle attitude
11. Frame dependence of the time derivative
12. Earth's orientation in space, and time on Earth
13. Orbital mechanics
14. Rigid-body dynamics
15. Modelling the motion and attitude of a vehicle
16. Concepts of tensor analysis
Index.

Subject Areas: Applied physics [PHV]