What are the uses of quaternions in Physics?

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Discussion Overview

The discussion focuses on the applications of quaternions in physics, particularly in mechanics and their potential uses in various fields such as computer graphics. Participants express interest in learning more about quaternions and their relevance in different contexts.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks resources for learning about the applications of quaternions in physics, particularly at the undergraduate level.
  • Another participant mentions that quaternions are used to express rotations and references a link to geometric algebra, suggesting it may be broader and more useful than quaternions.
  • A different participant notes the absence of quaternions in classical mechanics literature and expresses interest in their application in advanced topics like instanton solutions in gauge theories.
  • One participant advises looking into computer graphics literature, highlighting the use of quaternions in video games.

Areas of Agreement / Disagreement

Participants express varying levels of familiarity and interest in quaternions, with some suggesting they have practical applications while others question their mainstream relevance. No consensus is reached regarding the value of geometric algebra compared to quaternions.

Contextual Notes

Some participants express uncertainty about the mainstream acceptance of geometric algebra and its relevance to their education, indicating a potential limitation in the discussion of quaternions.

C.E
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Hi, I really want to learn about the applications of quaternions in Physics (I have posted in this section as apparently they can be used a lot in Mechanics). Anyway I was wondering if anyone knew of any good books (Undergraduate level),websites or interesting facts about this topic.
 
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I don't know much about them but I heard that they are used to express rotations. you might want to look at this:
http://modelingnts.la.asu.edu/

the above link is about 'geometric algebra' which is, like quaternions, an extension of the concept of imaginary numbers which involves the idea of rotations. but it seems to be broader and possibly more useful than quaternions (as you can see from the links on that page)
 
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I have never seen quaternions in mathematical classical mechanics books (Arnold, Abraham) but I would be interested if anyone knows of a quaternionic discussion along these lines.

It goes a little beyond the undergraduate level, but quarternions are the natural way to express instanton solutions in classical yang-mills SU(2) gauge theories (which are like a more advanced version of Maxwell's equations) cf Atiyah 1979.

I just want to comment that 'geometric algebra' is not a mainstream topic, and that personally I regret the time I've wasted on these kinds of things during my education. Until the math dept offers a class on geometric algebra, I don't recommend bothering with it.
 
You might try looking at the computer graphics literature. Quaternions are used in video games.
 

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