Using Lagrange principle for solving two-dimensional integral equation with a positive kernel

2015 ◽  
Vol 24 (5) ◽  
pp. 811-831 ◽  
Author(s):  
Y. Zhang ◽  
D.V. Lukyanenko ◽  
A.G. Yagola
Keyword(s):  
Integral Equation ◽  
Two Dimensional ◽  
Lagrange Principle ◽  
Positive Kernel ◽  
Dimensional Integral

Nonaxisymmetric Annular Punch Problem

1991 ◽  
Vol 58 (4) ◽  
pp. 947-953
Author(s):  
V. I. Fabrikant
Keyword(s):  
Integral Equation ◽  
Potential Theory ◽  
Two Dimensional ◽  
Title Problem ◽  
Annular Punch ◽  
First Time ◽  
Dimensional Integral ◽  
Punch Problem

A general formulation is given for the first time to the title problem. The method is based on the new results in potential theory obtained by the author earlier. The problem is reduced to a two-dimensional integral equation with an elementary kernel. Several specific examples are considered.

Lifting Surface Theory for the Problem of an Arbitrarily Yawed Sinusoidal Gust Incident on a Thin Aerofoil in Incompressible Flow

1970 ◽  
Vol 21 (2) ◽  
pp. 182-198 ◽  
Author(s):  
J. M. R. Graham
Keyword(s):  
Integral Equation ◽  
Kernel Function ◽  
Incompressible Flow ◽  
Velocity Component ◽  
Normal Velocity ◽  
Two Dimensional ◽  
Surface Theory ◽  
Equation Solution ◽  
Chebyshev Expansion ◽  
Dimensional Integral

SummaryThe solution to the problem of the loading generated on a two-dimensional thin aerofoil by an incompressible flow whose normal velocity component is of the general form exp [i(λx+/μy — ωt)] is calculated. The method used extends the two-dimensional integral equation solution for the induced vorticity by means of a Chebyshev expansion of part of the kernel function. Thin aerofoil approximations are made throughout, but no collocation procedure, as such, is required.

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