# Zhukovskii function

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The rational function of the complex variable . It is important for its applications in fluid mechanics, which were discovered by N.E. Zhukovskii (see , ), particularly in constructing and studying the Zhukovskii profile (Zhukovskii wing). Suppose that a circle is given in the -plane passing through the points (Fig. a), together with a circle touching on the outside at , with centre and radius . Under the mapping , the image of is a closed curve with a cusp at the point , touching an arc of the circle (the image of ) at that point; this image is represented in Fig. band is the Zhukovskii profile. Figure: z099280a Figure: z099280b

The function maps the exterior of the unit circle in the -plane to the exterior of . To obtain a Zhukovskii profile of a more general shape and disposition, the generalized Zhukovskii function is applied (see , , ): How to Cite This Entry:
Zhukovskii function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Zhukovskii_function&oldid=16495
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article