UDC 519.85
1 V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine
 stetsyukp@gmail.com
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3 V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine
khomiak.olha@gmail.com
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CONSTRUCTING THE EXTERNAL CONTOUR OF THE FRANKL NOZZLE USING
S-SHAPED CURVES WITH QUADRATIC DISTRIBUTION OF THE CURVATURE
Abstract. A mathematical model, algorithm, and software are developed for the problem of constructing an S-shaped curve,
which passes through two given points with given tangent inclination angles at them and provides a given tangent inclination angle
at a point with a given abscissa. To control the inflection point of the S-shaped curve with quadratic distribution of curvature
in natural parameterization, the tangent inclination angle at the point with the known abscissa is used. The algorithm is based
on a modification of the method with space dilation in the direction of the difference of two successive generalized gradients.
Computational experiments have shown the efficiency of the developed algorithm for constructing the external contour of a Frankl-type nozzle.
Keywords: external nozzle contour, S-shaped curve, natural parameterization, quadratic curvature, nonsmooth optimization, r -algorithm.
FULL TEXT
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