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Re: coordinate transformation

• To: mathgroup at smc.vnet.net
• Subject: [mg13169] Re: [mg13117] coordinate transformation
• From: Sean Ross <seanross at worldnet.att.net>
• Date: Mon, 13 Jul 1998 07:42:18 -0400
• References: <199807070744.DAA15613@smc.vnet.net.>
• Sender: owner-wri-mathgroup at wolfram.com

S.-Svante Wellershoff wrote:
> 
> Can someone explain me, how to use mathematica for transformations
> between
> different coordinate systems?
> 
> Like (x,y,z) in carthesian equals (r sin t cos p, r sin t sin p, r cos
> t) in spherical system.
> 
> Thanks, Svante
> 
> p.s.: hope its no faq!
> 
> ---------------------------------------------------------------------
>   S.-Svante Wellershoff      svante.wellershoff at physik.fu-berlin.de
>                              http://www.physik.fu-berlin.de/~welle/
> ---------------------------------------------------------------------
>   Institut fuer Experimentalphysik
>   Freie Universitaet Berlin         phone +49-(0)30-838-6234 (-6057)
>   Arnimallee 14                     fax   +49-(0)30-838-6059
>   14195 Berlin - Germany
> ---------------------------------------------------------------------

There is an add-on package which does this called
Calculus`VectorAnalysis`.  Please be careful.  Your definition above
and the ones built in to mathematica and the ones quoted in nearly
every physics book I have ever seen are valid only for vectors of
infinitesimal spatial extent(field vectors, not displacement vectors)
centered at the origin.  You must also transform the unit vectors along
with the components.  If you do any subsequent vector differential
operations, you must also take into account the coordinate metric which
depends on the unit system and the location of the vectors.

• References:
  • coordinate transformation
    • From: "S.-Svante Wellershoff" <svante.wellershoff@physik.fu-berlin.de>