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MathGroup Archive 1993

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Re: Oblate Spheroidal Coordinates

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: Re: Oblate Spheroidal Coordinates
  • From: keiper
  • Date: Tue, 13 Jul 93 07:28:42 CDT

	> It does not tell me direction cosines between the unit vectors
	> cartesian and oblate spheroidal coordinates.

I am not exactly sure what you want, but isn't this closely related to
what you want:

In[2]:= ??JacobianMatrix
JacobianMatrix[pt] gives the Jacobian matrix of the transformation from the
   default coordinate system to the Cartesian coordinate system at the point
   pt.  JacobianMatrix[pt, coordsys] gives the Jacobian matrix of the
   transformation from the coordinate system coordsys to the Cartesian
   coordinate system at the point pt.  If pt is not given, the default names
   of coordinate variables are used.

Attributes[JacobianMatrix] = {Protected, ReadProtected}
 
In[2]:= JacobianMatrix[{xi, eta, phi}, OblateSpheroidal]

Out[2]= {{-(Cos[phi] Cosh[eta] Sin[xi]), Cos[phi] Cos[xi] Sinh[eta], 
 
>     -(Cos[xi] Cosh[eta] Sin[phi])}, 
 
>    {-(Cosh[eta] Sin[phi] Sin[xi]), Cos[xi] Sin[phi] Sinh[eta], 
 
>     Cos[phi] Cos[xi] Cosh[eta]}, {Cos[xi] Sinh[eta], Cosh[eta] Sin[xi], 0}}

Jerry B. Keiper
keiper at wri.com
Wolfram Research, Inc.





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