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The researchers in Aerodynamics know that there is not a unitary
method of investigation in this field. The first mathematical model
of the air plane wing, the model meaning the integral equation
governing the phe nomenon, was proposed by L. Prandtl in 1918. The
integral equation deduced by Prandtl, on the basis of some
assumptions which will be specified in the sequeL furnishes the
circulation C(y) (see Chapter 6). U sing the circulation, one
calculates the lift and moment coefficients, which are very
important in Aerodynamics. The first hypothesis made by Prandtl
consists in replacing the wing by a distribution of vortices on the
plan-form D of the wing (i. e. the projection of the wing on the
plane determined by the direction of the uniform stream at infinity
and t he direction of the span of the wing). Since such a
distribution leads to a potential flow in the exterior of D and the
experiences show that downstream the flow has not this character,
Prandtl introduces as a sup plementary hypothesis another vortices
distribution on the trace of the domain D in the uniform stream.
The first kind of vortices are called tied vortices and the second
kind of vortices are called free vortices."
The book provides a solid and unitary mathematical foundation of
the basic and advanced principles of aerodynamics. The densities of
the fundamental solutions are determined from singular integral
equations. The fundamental solutions method in aerodynamics was
considered for the first time and used by the author in over 30
papers published in prestigious journals (e.g. QAM, AIAA, ZAMM,
etc) in order to develop a unitary theory. The boundary element
method is used for numerical approximations in compressible
aerodynamics. The text incorporates several original contributions,
among other traditional mathematical methods.
The book also represents a comprehensive presentation of research
results since the seminal books on aerodynamics of Ashley and
Landahl (1965) and Katz & Plotkin (1991).
A rigorous mathematical approach is used to present and explain
classic and modern results in this field of science. The author has
therefore conceived several appendices on the Distribution Theory,
the singular Integral Equations Theory, the Finite Part, Gauss
Quadrature Formulae, etc.
The book is concluded by a relevant bibliographical list which is
especially useful for researchers.
The book is aimed primarily at applied mathematicians, aeronautical
engineers and space science researchers. The text may be used also
as a comprehensive introduction to the mathematical foundations fo
aerodynamics, by graduate students n engineering and fluid dynamics
with a strong mathematical background.
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