PDFs for further reading
The entire site is available a number of ways. As a book:
Put the site on your own computer. At the command line, run:
git clone https://github.com/dougsweetser/Q.git
A collection of 6 problem sets solved using only real-valued quaternions is available for $1.99 as a pdf, epub, or mobi file
Bits of this site
- Space-times-time invariance as gravity in 2 pages - 2 pages
- Where quaternions fit - 1 page
- Space-time equivalence classes - 10 pages
- Space-time Geometries - 1 page
- Quaternion space-times-time invariance as gravity - 7 pages
- Deriving the Maxwell source equations by hand - 1 page
- PGT - Personal Gravity Theory Homework Assignment - 1 page
Other people's efforts
- Gauss's notebook - Written in 1819, published 1900, 6 pages. All calculations, no discussion.
- Sudbery's first paper, "Quaternion Analysis", memo, 1977, 44 pages, on why quaternion analysis is no good.
- Sudbery's second paper, same title, 1979, 28 pages on the topic. Please look to my work above on quaternion analysis for a much better alternative!.
- C. A. Deavours paper, "The Quaternion Calculus". My critique is that using his definition of a quaternion derivative, if a function like f=q is analytic in q, f^2 is not. That indicates a better definition must be found before quaternion analysis can really begin.
- Salamin's paper, "Application of quaternions to computation with rotations", (1979, 9 pages) on rotations. Howell and Lafon's paper, 1975, 13 pages, on the efficiency of quaternion multiplication.
- Silberstein's paper, "Quaternionic Form of Relativity", 1912, 20 pages, on using biquaternions for quaternion special relativity. Biquaternions are NOT a division algebra, and are not used in any operations on this web site.
Resources on gimble lock, a problem that arises from not using quaternions for 3D rotations, links provided by Alex Green:
Bottom line: always avoid Euler angles.