Elliptic functions and integrals with real modulus in fluid mechanics


naca-tm-1435
1958


The usefulness of the Schwarz transformation and elliptic functions in defining flows outside and inside polygons is duscussed and illustrated. The mathematical properties and physical significance of the elliptic integrals of the first, second, and third kinds and of the elliptic funcitons are examined, together with their relations to the theta and zeta functions. Applicaitons of the various funcitons are made to the calculation of wing profiles, of compressor profiles, and to the study of the vibration of airplane wings and of compressor vanes.

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