Rotation Sequences and the Theory of Vectors and Coordinates

Don Koks (Autor)

Buch | Hardcover

566 Seiten

2025
Cambridge University Press (Verlag)
978-1-009-51675-4 (ISBN)

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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.

Don Koks has a doctorate in quantum cosmology, with a background in pure and applied mathematics and physics, and applied accelerator physics. In his 20 years in Australian Defence he specialised in radar signal processing, spatial orientation concepts, relativistic precision timing, orbital mechanics and target tracking. His previous two books are 'Explorations in Mathematical Physics' (2006) and 'Microstates, Entropy and Quanta' (2019), both published by Springer.

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.

Erscheinungsdatum	15.04.2025
Zusatzinfo	Worked examples or Exercises
Verlagsort	Cambridge
Sprache	englisch
Maße	170 x 244 mm
Gewicht	1211 g
Themenwelt	Mathematik / Informatik ► Informatik ► Grafik / Design
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Physik / Astronomie ► Angewandte Physik
	Naturwissenschaften ► Physik / Astronomie ► Astronomie / Astrophysik
ISBN-10	1-009-51675-2 / 1009516752
ISBN-13	978-1-009-51675-4 / 9781009516754
Zustand	Neuware