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Author: ozogg
Time: 03/28/01 22:32 PST
This is a reply to message no. 6048 by james007
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Current Topic:
Rotation as a vector
29 March, 2001:

In response to the thread about "rotation as a vector," last addressed by :
      Author: james007
      Posted on: 02/09/01 11:42 PST
      In reply to message no. 6049 by dr funda.

Let me first clear up some shoddy language usage.
The initial question asked:
      "if rotation was a vector."
This question is unclear, for it should ask:
      "which of angular
            displacement,
            velocity,
            acceleration,
      are vectors?"  

The quick answer is:
      "the first is not."

A slightly longer answer would add:
      "the second two are."

Longer again would say:
      "go consult pp.324 - 325 of
      Pure and Applied Mathematics,
      HALSTEAD & HARRIS,
      Macmillan & Co,
      Melbourne, Australia, 1963"
On p.324, this text gives a cogent proof that for small angular displacement, a Pythagorean identity can apply for compounding angles in 3D, i.e.
      A^2 = B^2 + C^2

An even longer answer adds:
      "go consult p.296 - 300
      Advanced Engin'g Mathematics,
      KREYSZIG, Erwin,
      John Wiley & Sons,
      New York, USA, 1962"

Finally I would add:  
"Both references, like the initial questioner, are also shoddy in using
the word as an unclear muddling of the three and
angular quantities."

These are ancient texts I admit, from way back when I did my first tertiary
qualification, in the early 60's.  More recent text incarnations will say
the same thing.  Certain fundamentals will NEVER change, like Ohms Law.

I still possess every text from every course I have ever done,
with heavy marginal annotations, copious underlining, and now heavy
highlighting.  Don't let anyone tell you that education is wasted.

Cheers,
Colin
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