From: Janek Kozicki (janek_listy_at_[hidden])
Date: 2006-06-13 11:31:58
Andy Little said: (by the date of Tue, 13 Jun 2006 00:59:11 +0100)
> > There are also spaces where the units (or more accurately, the
> > dimensions) are not the same in all directions, so any vectors in those
> > spaces will have mixed units in any coordinate system. A commonly used
> > one is called "phase space" and it includes the position and momentum
> > variables for a system all in the same space. Thinking of them together
> > turns out to be quite important in some applications, so the example can
> > be quite meaningful for some people.
> That is interesting, though I find anything beyond the usual space difficult to
> visualise. The ability to visualise things such as this seems to be what marks
> out mathematicians.
... and engineers? physicians? I'm not sure to which category I could
belong (certainly not mathematician) but "phase space" is quite common
when working with engineering problems. It is the most handy way to
represent what is going on in any given point of space. However vector
operations between vectors in "phase space" are different than
dot_product and cross_product. Those two operations make no sense in fact.
It is although common to multiply such vectors by some matrices...
-- Janek Kozicki |
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