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I've been studying Quaternions for a week, on my own. I've learned various facts about them but I still don't understand them. My goal is to understand rotation quaternions specifically. I don't want to just memorize the formulas for using rotation quaternions, I want to truly understand them.

It's the most difficult thing I've ever tried to learn. Does anyone know any good resources for understanding quaternions?

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You may find good explanation here mathworld.wolfram.com/Quaternion.html –  Mathlover Mar 15 '13 at 9:17
    
I can recommend the book "Naive Lie Theory" by John Stillwell. –  Hauke Strasdat Sep 3 '13 at 6:07

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One piece of quick advice before I recommend stuff on quaternions. Understand how complex numbers produce rotations in the complex plane first. Maybe you've already done that... if so, that'll be a helpful foothold.

Several questions on this site might be helpful:

How do quaternions represent rotations?

How can one intuitively think about quaternions?

How do you construct the quaternion and the multiplication rules, like Hamilton did?

Is there a geometric realization of Quaternion group?

Quaternions and Rotations

Then there is the wiki page devoted to this topic:

http://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation

If you have funds and patience there are a few books:

http://www.amazon.com/Quaternions-Octonions-John-Horton-Conway/dp/1568811349/ref=sr_1_5?ie=UTF8&qid=1363353978&sr=8-5&keywords=quaternions+and+rotations

http://www.amazon.com/Quaternions-Rotation-Sequences-Applications-Aerospace/dp/0691102988/ref=sr_1_1?ie=UTF8&qid=1363353978&sr=8-1&keywords=quaternions+and+rotations

http://www.amazon.com/Rotations-Quaternions-Double-Groups-Mathematics/dp/0486445186/ref=sr_1_2?ie=UTF8&qid=1363353978&sr=8-2&keywords=quaternions+and+rotations

One more thing: if you've only been studying it for a week, don't get discouraged! There is no reason to expect that you will get it all completely so quickly. I took up the same task that you are describing several months ago. I've had a lot of fun picking up the basic idea, and I'm still learning a lot about it all the time. Even after this time, I would not say I "truly understand them," but I definitely have a better grip on quaternions and their relationship to rotations.

As the old saying goes, "Don't worry about going slowly, worry about standing still."

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Quaternions need not be difficult or overwhelming; they are really quite simple. Most of the complexity is generated by writers who primarily want to impress readers with the magnificence of their own intellect. Go to my website, noelhughes.net and start with the quaternion training link. See if it helps.

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I think this answer is acceptable, but please bear in mind that some people may consider this as self-advertisement. –  Mårten W Aug 31 '13 at 22:03

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