Joukowski Conformal Ellipse and Critical Slit
Turn circles into ellipses and discover where a conformal map folds a boundary into a slit.
Free theory articleTurn circles into ellipses and discover where a conformal map folds a boundary into a slit.
Concept & interpretation
The Joukowski transformation maps the exterior of the unit circle to the exterior of a critical slit, and concentric larger circles to ellipses. It is an important conformal mapping used in aerodynamics.
experiment
In the Joukowski Conformal Ellipse and Critical Slit module, explore the conformal mapping of circles to ellipses and the degenerate critical slit.
To observe the critical endpoint, follow these steps to see where conformality fails:
- Set the Circle radius control to 1.
- Set the Angle degrees control to 0.
- Note that the mapped coordinates become (2, 0) and the derivative becomes 0, indicating the conformal mapping fails here.