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Re: Should RotationMatrix work with symbolic vectors?

• To: mathgroup at smc.vnet.net
• Subject: [mg85995] Re: Should RotationMatrix work with symbolic vectors?
• From: "Fred Klingener" <gigabitbucket at gmail.com>
• Date: Sat, 1 Mar 2008 04:39:17 -0500 (EST)
• References: <fq5qdj$kol$1@smc.vnet.net>
• Reply-to: "Fred Klingener" <gigabitbucket at gmail.com>

"Steve Gray" <stevebg at roadrunner.com> wrote in message 
news:fq5qdj$kol$1 at smc.vnet.net...
> It works fine when the "source" and "destination" vectors are  numeric
> (it gives a matrix, say rm2, such that rm2.a2 is parallel to b2):
>
> a2 = {1, 2, 3};
> b2 = {3, 5, 7};
> rm2 = N[RotationMatrix[{a2, b2}]]
>
> {{0.997846,  0.028474, 0.059102},
> {-0.0301974, 0.999138, 0.028474},
> {-0.0582406,-0.0301974,0.997846}}
>
> and
>
> Normalize[rm2.a2]              (* rm2.Normalize[a2] also works *)
> {0.329293, 0.548821, 0.76835}
>
> which is a unit vector parallel to b2. So far, great. But unless a2
> and b2 have numeric values, RotationMatrix does nothing.
>
> avec = {a2x, a2y};
> bvec = {b2x, b2y};
> RotationMatrix[{avec, bvec}]   (* gives *)
>
> RotationMatrix[{{a2x, a2y}, {b2x, b2y}}]
>
> Can't it handle symbolics like most functions?

I can't offer much beyond commiseration and a confession that I've given up 
trying to get some of Mathematica's higher order geometric functions working the way I want them to.

I've taken to doing things at a lower level where I can get my own 
vectorSimplify (say) pattern replacements working.

My approach so far is pretty ad hoc, devoted to unraveling cross products 
that escaped HoldForms and to casting geometric problems in a form that 
simplifying scalar and vector triple product expansions give useful answers. 
I haven't tried to pick apart the Mathematica transformation functions or symbolic matrix forms, because I'm after different fish.

I don't have a feel how I would approach a general vectorSimplify.

No much, but hth,
Fred Klingener