PDFs for further reading
The entire site is available a number of ways.
Avaible for $10 is a pdf, epub, or mobi file.
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
- 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
Other people's efforts
- 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 an algebraic field, 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.