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Elliptic Functions and Integrals with Real Modulus in Fluid MechanicsAdvantage of the elliptic functions and of the more general functions of Schwarz for fluid mechanics. Flows outside and inside polygons. Application to the calculation of an elbow diffuser for a wind tunnel. Properties of the elliptic integrals of the first kind and of the elliptic functions. Properties of the theta functions and decomposition of the elliptic functions into products of theta functions. Properties of the zeta functions. Decomposition of the elliptic functions into sums of zeta functions and calculations of the elliptic integrals. Applications to the calculation of wing profiles, of compressor profiles, and to the study of the vibrations of airplane wings and of compressor vanes. The manuscript of the present paper was checked by Mr. Eichelbrenner who corrected several imperfections and suggested numerous improvements to make reading of the paper easier. However, the limited subject does not permit filling in more than an incomplete knowledge of the properties of analytic functions.
Document ID
20030065802
Acquisition Source
Headquarters
Document Type
Other - NACA Technical Memorandum
Authors
Legendre, Robert (National Advisory Committee for Aeronautics Washington, DC, United States)
Date Acquired
September 7, 2013
Publication Date
June 1, 1958
Publication Information
Publication: Les Fonctions et Integrales Elliptiques a Module Reel en Mecanique des Fluids
Subject Category
Fluid Mechanics And Thermodynamics
Report/Patent Number
NACA-TM-1435
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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