Does anyone know any resources for Quaternions for truly understanding them?

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."


I know that I am very late in this response, and that probably you found some paths to follow on quaternions, however, I thought that you might like to know these original resources on quaternions that I discovered when doing my own research to learn about quaternions myself:

  1. An Elementary Treatise On Quaternions_Peter Guthrie Tait
  2. Introduction to Quaternions_Philip Kelland, Peter Guthrie Tait
  3. On Quaternions_William Rowan Hamilton
  4. Elements of Quaternions_William Rowan Hamilton

Also, to grasp Quaternions intuitively, I recommend this book that I recently found: Visualizing Quaternions by Andrew Hanson.

Best of luck in your learning ventures!