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I have a problem with computing of $\alpha_{0}$ like on the figure for

joukowski[c_][{x_, y_}] := {x, y} + 1/(x^2 + y^2) {x, -y}

How to show on manipulate tangent line and change of $\alpha$ that $\alpha$ for this simulations:

Manipulate[
  Module[{radius = Max[Norm[{1, 0} - center], Norm[{1, 0} - center]], circle}, 
    circle = 1 {Cos[#], Sin[#]} + center &; 
    ParametricPlot[
      {circle[θ], joukowski[1][circle[θ]]}, {θ, 0, 2 π}, 
      PlotRange -> 2.5, 
      Epilog -> 
        {AbsolutePointSize[10], 
         Blue, Point[{1, 0}], Point[{-1, 0}], 
         Red, Circle[{-0.2, 0.2}, 0.08], 
              Circle[{-0.2, 0.2}, 0.05], 
              Circle[{-0.2, 0.2}, 0.02], 
              Line[{{-0.2, 0.1}, {-0.2, 0.3}}], 
              Line[{{-0.3, 0.2}, {-0.1, 0.2}}]}, 
      PlotStyle -> {{Thick, Blue}, {Thick, Red}}, 
      ImageSize -> {480, 480}]], 
  {{center, {0, 0}}, Locator}, 
  SaveDefinitions -> True]

enter image description here

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4
  • $\begingroup$ Are you trying to replicate the figure? There are four transformations, not one. Do you want just the top two? Or just the top right one? You can arrange multiple plots with Grid or GraphicsGrid. -- Is it also that you do not know how to calculate the tangent line? Or is that you do not know how to plot the equation? -- Finally, a third possibility is that you do not know how to use Arrow to make the double-arrow angle markers? -- -- One other thing that is not clear to me is how the point of tangency is determined. In your Manipulate the curve moves about. $\endgroup$
    – Michael E2
    Nov 24 '19 at 14:24
  • $\begingroup$ I find this question unclear. I am unable to relate your code in a meaningful way to the diagram that follows it. $\endgroup$
    – m_goldberg
    Nov 24 '19 at 14:50
  • $\begingroup$ You may be interested in mathematica.stackexchange.com/q/119516/27951 and mathematica.stackexchange.com/q/84593/27951 $\endgroup$
    – MarcoB
    Nov 24 '19 at 20:43
  • 1
    $\begingroup$ If you search this site for "manipulate tangent line" you will find several relevant answers. A recent one is How to shorten ... tangent line $\endgroup$
    – LouisB
    Nov 24 '19 at 22:07

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