# Applications of quaternions

1. Jan 11, 2005

### Raparicio

In my infinite curiosity, I am reading about quaternions and his algebra. I have readed that they are used principally in "pure mathmatics", but there are applications in 3D modelling, and others... there are applications to the physics?

2. Jan 11, 2005

### marlon

GOOD question.

Just goto the "info on the web" entry. You will find a link there entitled "doing physics with quaternions"

https://www.physicsforums.com/journal.php?s=&action=view&journalid=13790&perpage=10&page=4 [Broken]

marlon

basically quaternions are an extension of complex numbers. So in stead of some complex number a+ib (with i² = -1) you now write a+ib+jc+kd. Where a,b,c,d are real numbers and i²=j²=k²=-1 and ij=k=-ji and jk=i and so on

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3. Jan 11, 2005

### Raparicio

Thanks You

Last edited by a moderator: May 1, 2017
4. Jan 11, 2005

### marlon

my pleasure

marlon

5. Jan 11, 2005

### dextercioby

1.Quaternions have been discovered in 1844 by Sir William Rowan Hamilton.
Here u have all articles published by W.R. Hamilton,bith in physics and maths,including the ones about quaternions (round 30 articles) and their applications.

2.What Marlon didn't tell u (i hope he knows,though :tongue2: ) is that without the wonderful work by Ricci-Curbastro,H.Weyl,T.Levi-Civita,Christoffel and H.Minkowski,we would be using quaternions in modern physics intstead of 4-vectors...

Daniel.

6. Jan 11, 2005

### marlon

and Gauss and Riemann and ...

marlon

7. Jan 12, 2005

### Raparicio

4-vectors

What's the difference between 4-vectors and quaternions? are they changeables?

8. Jan 12, 2005

### dextercioby

Well,yes,as u might have figured out from the link Marlon gave you,u can do pretty much the same thing with 4-vectors and qaternions.The problem appears when u try to enlarge/restrain the vector space.Quaternions are meant for 4 dimensions.Hence the name...Would it make sense to build another field of numbers called "n-ions",just to try to duplicate the wonderful things done with vectors???I doubt it...

Daniel.

9. Jan 12, 2005

### remcook

I know quaternions are used quite a lot in attitude control problems of satellites and aircraft.

10. Jan 12, 2005

### BobG

And in three-dimensional graphics for simulations and video games. Quaternions avoid the problem you run into with singularities when using Eulerian rotations. (You might remember that scene from Apollo 13 where they're manually controlling the spacecraft and trying to avoid gimbal lock - that's what they're talking about - singularities, that is; not quaternions.)

11. Jan 12, 2005

### Raparicio

Quaternions

Are good books about quaternions? I'm interested in basic, middle and high level of mathmatics.

12. Jan 12, 2005

### jcsd

And I suppose this is exactly why we prefer vectors to quartenions after all there's not much. that the quarternions can do that vector spaces can't.

In a sense there are such thing as 'n-ions' they are called Cayley-Dickson constructions (or really 2n-ions in the sense that the nth construction forms a 2n-dimensional real vector space) for n = 1,2 they are just the complex numbers and quarternions respectively.

John Baez has a part of his site about hypercomplex numbers (more specifically the octonions) at his site:

http://www.math.ucr.edu/home/baez/Octonions/octonions.html [Broken]

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13. Jan 12, 2005

### quasar987

What is the name of the 2^4-ions?

14. Jan 12, 2005

### jcsd

Sedenions I believe.

15. Jan 13, 2005

### BobG

Quaternions and Rotation Sequences : A Primer with Applications to Orbits, Aerospace and Virtual Reality by JB Kuipers.

He wrote it for the Air Force, so it provides a little more complete package. It provides a little refresher knowledge on vectors, rotation sequences, a little help on quaternion math, etc. in addition to the applications, which are towards the end of the book.

The soft cover edition (I don't even know if there's a hard cover edition) is less than \$40 (US).

16. Jan 13, 2005

### Clausius2

I only have heard about quaternions in Hamiltonian Mechanics. Anyway, my main purpose is to greet my colleague:

Bienvenido al mundo de los locos, Raparicio!

17. Jan 13, 2005

### Raparicio

Hello Clausius2 and forum.

An interesting question about quaternions is: can be writted the Reynolds transport formulae in quaternions?

Clausius2, lo mismo digo!!!

18. Jan 14, 2005

### Clausius2

I don't undertstand that. Are you refferring to the Reynolds Averaged N_S equations?. With what purpose do you want to make that?.

19. Jan 14, 2005

### Raparicio

Practising Quaternions

I'm practising with quaternions, and this formulae is like a addition of quaternions... I think it's very interesting, but my level is not very high.

best reggards...