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From: Geoffrey Irving (irving_at_[hidden])
Date: 20060612 11:17:51
On Mon, Jun 12, 2006 at 11:10:14AM 0400, John Phillips wrote:
> Andy Little wrote:
> >
> > Having only investigated transform matrices, I had hoped that integrity of
> > quantities can be maintained in most cases. But I havent done extensive
> > experiments
> >
> > In cases of vectors, I have only used vectors where all elements are one type of
> > quantity. The vectors are used to represent position, direction and so on in 3
> > dimensions. A container that holds different quantities I would consider to be a
> > tuple. But I stress I am not an expert.
> >
> > [...]
> >
> >
> > regards
> > Andy Little
>
> I think the question of even a position vector depends on what
> coordinate system you choose. In cartesian coordinates, all of the
> components of the vector have the same units, but in any other system
> (spherical, or cylindrical, for example) the components don't all have
> the same units. Since the coordinate system is another thing that should
> be problem dependent, even simple vectors like the position of a
> particle may have mixed units.
>
> John Phillips
The vector type models vector spaces written in component form, so it can't
correctly be used for spherical or cylindrical coordinates. Tuples should
suffice for those systems. Are there useful linear coordinate systems with
different units? Hmm. I suppose spacetime counts, which is probably
something you care about quite a bit.
Of course, when computing in spacetime, you probably use the same units for
time and space anyways...but I'll have to defer to you on that one.
Geoffrey
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