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Re: Can't quite figure out tensors

  • To: mathgroup at smc.vnet.net
  • Subject: [mg96973] Re: Can't quite figure out tensors
  • From: Roland Franzius <roland.franzius at uos.de>
  • Date: Sat, 28 Feb 2009 06:44:35 -0500 (EST)
  • References: <go8in6$lg2$1@smc.vnet.net>

Aaron Fude schrieb:
> Hi,
> 
> I'm trying to write code that will produce Christoffel symbols for
> various coordinate systems. I would like to use the definition that
> yields Gamma_ij^k as the partial of the covariant basis e_i with
> respect to variables x^j dotted with the contravariant vector e^k. So
> far I have
> 
> z[r_, theta_] := {r Cos[theta], r Sin[theta]}
> ei[r_, theta_] := {Derivative[1, 0][z][r, theta],
>   Derivative[0, 1][z][r, theta]}
> gij[r_, theta_] := ei[r, theta].Transpose[ei[r, theta]]
> gIJ[r_, theta_] := Inverse[gij[r, theta]]
> deidxj[r_, theta_] := {Derivative[1, 0][zi][r, theta],
>   Derivative[0, 1][zi][r, theta]}
> 
> and now i need to form the tensor product
> deidxj * gIJ * ei
> 
> and it has proven to be a bit to intense for me to pull off. Could
> someone show me how to do that?
> 
> Many thanks in advance,

Look for the Christoffel and related functions from General Relativity 
in the example notebooks of

Zimmerman/Olness
Mathematica for Physicists

You can download the notebooks from

http://library.wolfram.com/infocenter/Books/4539/

-- 

Roland Franzius


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