Quaternions in Joukowski Transformation
Jeyabalan, Simon (2011)
2011
Master's Degree Programme in Information Technology
Luonnontieteiden ja ympäristötekniikan tiedekunta - Faculty of Science and Environmental Engineering
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Hyväksymispäivämäärä
2011-12-07
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:tty-201205161130
https://urn.fi/URN:NBN:fi:tty-201205161130
Tiivistelmä
Conformal mappings have been exploited for a long time in a number of physical problems arising in aerodynamics, thermal equilibrium, electrostatics, fluid flow and so on. These complex-valued functions are implemented with just a single complex variable z. However, in this study, quaternions are introduced into a Joukowski transformation, a conformal map used in the study of fluid flow around airfoils. Analysis is effected so as to determine the properties of this transformation function and spheres of both Euclidean and hyperbolic geometry are executed in this expedition.