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Thanks Daniel! I am actually interested in the inverse of the last map in the notebook ((xd, yd) ---> (xa, ya)), which maps the circular annulus to the airfoil annulus. So I would like to find an expression for the inverse map ((xa, ya) ---> (xd, yd)). What you have solved is the inverse mapping of a circular disk to a circular annulus, which was just a step that I use to generate a circular annulus before mapping it to an airfoil annulus. I will try your approach to see if it helps in finding the inverse map of interest..... Thanks again, Saliou

POSTED BY: SALIOU TELLY

Daniel Lichtblau

Daniel Lichtblau, Wolfram Research

Posted 9 years ago

POSTED BY: Daniel Lichtblau

Kay Herbert

Kay Herbert, Chief scientist, Sloan Valve Co.

Posted 9 years ago

POSTED BY: Kay Herbert

SALIOU TELLY

Posted 9 years ago

POSTED BY: SALIOU TELLY

Kay Herbert

Kay Herbert, Chief scientist, Sloan Valve Co.

Posted 9 years ago

All depends, but usually you get an answer if it exists. Example: In[9]:= Solve[w == (z - z0)/Abs[z] + 1/(z Abs[z]), z] Out[9]= {{z -> (z0 - Sqrt[-4 - 4 w + z0^2])/(2 (1 + w))}, {z -> ( z0 + Sqrt[-4 - 4 w + z0^2])/( 2 (1 + w))}, {z -> (-z0 - Sqrt[-4 + 4 w + z0^2])/( 2 (-1 + w))}, {z -> (-z0 + Sqrt[-4 + 4 w + z0^2])/(2 (-1 + w))}} You can also try Reduce

All depends, but usually you get an answer if it exists. Example:

In[9]:= Solve[w == (z - z0)/Abs[z] + 1/(z Abs[z]), z]

Out[9]= {{z -> (z0 - Sqrt[-4 - 4 w + z0^2])/(2 (1 + w))}, {z -> (
   z0 + Sqrt[-4 - 4 w + z0^2])/(
   2 (1 + w))}, {z -> (-z0 - Sqrt[-4 + 4 w + z0^2])/(
   2 (-1 + w))}, {z -> (-z0 + Sqrt[-4 + 4 w + z0^2])/(2 (-1 + w))}}

You can also try Reduce

POSTED BY: Kay Herbert

SALIOU TELLY

Posted 9 years ago

Thanks Kay! This seems promising as it does appear to be able to solve in the complex form. I will look into the solution in more detail for correctness and also see if I can re-express it in Cartesian form, which is really the ideal form that I would need to work with. I am more of a Matlab person but I am amazed by the power of Mathematica when it comes to symbolic calculations..... Thanks again for your time, Saliou