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Re: Quaternion problem

• To: mathgroup at smc.vnet.net
• Subject: [mg67446] Re: Quaternion problem
• From: Roger Bagula <rlbagula at sbcglobal.net>
• Date: Sun, 25 Jun 2006 03:19:06 -0400 (EDT)
• References: <e7ap5q$952$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Staffan Langin wrote:

>Hello,
>
>I'm a total Mathematica newbee so please bear with me :-). I'm trying to let 
>Mathematica analytically evaluate a second order derivative for me. The 
>function has several parameters with some of them being of 
>"Quaternion-type". I want to instruct Mathematica that the commutative rule 
>doesn't apply when evaluation the function. Is that possible? Thanks in 
>advance.
>
>Staffan Langin
>
>  
>
I thought I'd wait on this and see if anybody else took it up.
In my experience using the 2by2 matrix version of a quaternion is more 
likely to work
in differential equations than the built in Quaternion[a,b,c,d] function.
Getting back to quaternion form can be hard though from the matrices.
I gave it in a post on matrix substitution recently above.
The best I can tell you is that you have to "Shepard"
any such calculation in Mathematica because it may do something 
systematic and unexpected
to your equations. If you can, start as simple as possible and check by 
hand until
you get comfortable with the mechanics.
One way is to do the differentiation on functions outside of the 
quaternions.
Things like quaternion sine Gordons and D'Amlembertian operators can be 
tricky,
 but if you watch the results careful,
 it is possible to do amazing things with quaternions.
You should get familar with Yang-Mills gauge fields if you can.
Also you should think in terms of angles, rotations and angular momentum
and not in distance, velocity and translations term.
Roger Bagula