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Quaternions, the math and magic of rotational matrices
on March 28, 2014
Quaternions are an extremely arcane and difficult area to study. There are over a half dozen books in print covering the subject and getting a decent look at them without paying a hundred dollars is a small feat in itself. Altman's book does the job well without being long winded. It gives a thorough historical introduction and proceeds into the material at a comfortable pace while providing sufficient diagrams to keep the subject clear. At about 277 pages, it should provide several weeks of unraveling the puzzle before the reader manages to encompass the entire subject.
Quaternions supply the solution to avoiding "gimbal lock" when your rotational computation takes your Euler analysis into alligning two of your three rotational axies into the same plane. This effect makes your craft or creature rotation lockup during simulation and has caused more than one remotely piloted vehicle to crash. Avoid the embarrassment and avoid the whole problem by using Quaternions instead.
Unless you are an aeronautical engineer, you are probably looking into this book to support a computer game or are applying a factory furnace simulation for energetic particle flux in a chemical reactor or combustion engine. This material will support such activities well. You will probably need a serious GPU to serve up the vectorization on a half million molecules in those cases. You can use these equations to support kinematic simulations for electrodynamic forces in electric motors and propulsion systems. Just remember that electron spin is a quantum concept, the electrons don't actually have a rotational momentum as a top does.
If you need more graphic detailing to understand the subject, I recommend "Visualizing Quaternions", which has better graphics along with a heftier price. And in either case, you need to be comfortable with vector mathematics and matrix operations to avoid getting stuck in the middle of this material. Have a great time powering your simulations with this mathematical tool.