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Author: ozogg
Time: 12/14/03 18:52 PST
This is a reply to message no. 12814 by b1ueshift
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Rotation as a vector
OK, I'll grant that it is intuitively attractive to perceive an angular displacement of 10 degrees CW as a "vector" 10units long, pointing in the (RH) direction of the axis of rotation.

But when maths conceives of a number system, it doesn't do so in glorious isolation.  One has to "do things" with these numbers. like +-*/.

Likewise, vectors need to "do things", like obey rules for +-*/.

Take the first operator +.

A true vector can be added to another true vector to yield a composite vector that would achieve the same result as the two components applied separately.

It should not matter in which order the two component vectors are applied, and this is called the "law of commutativity."

Thus, vectors obey commutativity for the +,- operators, but not for */.

Your proposed "angular displacement" vector obeys none of the "rules of algebra";  it is therefore a concept that "does nothing" and cannot be used.

Hope that is a persuasive reason to now drop this foolish idea that "angular displacement is a vector".

As for your proposition about "sources of opinion", yes it is true that "experts can make mistakes", and SHOULD be challenged, but they tend to do so less frequently than self-opiniated ratbags.  That is why we demand qualifications before we allow anyone to build a bridge, or a plane, or take a scalpel to our bodies. And why we have (educated) editorial referees appointed to challenge any new theory wishing to be published.

And why we have a system of academic letters after names, as proof that a person has at least wrestled with the fundamental notions of their discipline, and has displayed a certain proficiency according to some accrediting educational authority.

Likewise, arrogant opinion is not the preserve only of experts; "nutters" are well known to proclaim they have the "answers to the universe" (and that everyone else is deceived).

I know whom I would rather have designing the planes I fly in !

B.Sc, Dip Elec Eng, Grad I.E.Aust, MIEEE, TTAV, MST-accr.
(but I would rather play the ball, than the man).
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