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MathGroup Archive 2007

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Coordinate conversion with Grad

  • To: mathgroup at smc.vnet.net
  • Subject: [mg75872] Coordinate conversion with Grad
  • From: laxmipt at gmail.com
  • Date: Sat, 12 May 2007 03:10:45 -0400 (EDT)

I am using Mathematica 5.2.
I wish to do coordinate transformations for differential geometry.
For
example transform a Grad from a cylindrical system to a Cartesian
system:
For example:
In[1]:= << Calculus`VectorAnalysis`;
SetCoordinates[Cylindrical]

Out[2]:=Cylindrical[Rr, Ttheta, Zz]

In[3]:= Grad[Cos[Ttheta], Cylindrical[Rr, Ttheta, Zz]]

Out[4]:={0,-Sin[Ttheta]/Rr,0}

The above Grad vector refers to the cylindrical system.  How can I get
Mathematica to convert it into the corresponding gradient in the
Cartesian
system, which would become:
{sin^2(Ttheta)/Sqrt[x^2+y^2], sin(Ttheta)Cos(Ttheta)/Sqrt[x^2+y^2],0}

Thanks!
Sachin



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