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.