Braga da Costa Campos Transcendental Representations with Applications to Solids and Fluids

Erscheinungsjahr 2012
ISBN: 978-1-4398-3524-1
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 898 Seiten

Reihe: Mathematics and Physics for Science and Technology

Building on the author’s previous book in the series, Complex Analysis with Applications to Flows and Fields (CRC Press, 2010), Transcendental Representations with Applications to Solids and Fluids focuses on four infinite representations: series expansions, series of fractions for meromorphic functions, infinite products for functions with infinitely many zeros, and continued fractions as alternative representations. This book also continues the application of complex functions to more classes of fields, including incompressible rotational flows, compressible irrotational flows, unsteady flows, rotating flows, surface tension and capillarity, deflection of membranes under load, torsion of rods by torques, plane elasticity, and plane viscous flows. The two books together offer a complete treatment of complex analysis, showing how the elementary transcendental functions and other complex functions are applied to fluid and solid media and force fields mainly in two dimensions.

The mathematical developments appear in odd-numbered chapters while the physical and engineering applications can be found in even-numbered chapters. The last chapter presents a set of detailed examples. Each chapter begins with an introduction and concludes with related topics.

Written by one of the foremost authorities in aeronautical/aerospace engineering, this self-contained book gives the necessary mathematical background and physical principles to build models for technological and scientific purposes. It shows how to formulate problems, justify the solutions, and interpret the results.

Zielgruppe

Practitioners and researchers in mechanics, fluid mechanics, and applied mathematics.

Autoren/Hrsg.

Braga da Costa Campos, Luis Manuel

Fachgebiete

• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Aerodynamik
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Strömungslehre
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Kontinuumsmechanik

Inhaltsverzeichnis

Sequences of Fractions or Products
Power Series, Singularities, and Functions
Series of Fractions for Meromorphic Functions (Mittag-Leffler 1876, 1884)
Meromorphic Function as a Ratio of Two Integral Functions
Factorization with Infinite Number of Zeros
Infinite Products for Circular Functions
Recurrence Formulas and Continued Fractions (Wallis 1656; Euler 1737)
Optimal and Doubly Bounded Sharpening Approximations
Transformation of Series and Products into Fractions (Euler 1785)
Continued Fraction for the Ratio of Two Series (Lambert 1770)
Conclusion

Compressible and Rotational Flows
Source, Sink, and Vortex in a Compressible Flow
Potential Vortex with Rotational Core (Rankine; Hallock and Burnham 1997)
Minimum Energy (Thomson 1849) and Intrinsic Equations of Motion
Laplace/Poisson Equations in Complex Conjugate Coordinates
Second Forces/Moment and Circle Theorems
Cylinder in a Unidirectional Shear Flow
Monopole Interactions and Equilibrium Positions
Cylinder in a Stream with Two Trailing Monopoles (Föppl 1913)
Reciprocity Theorem (Green 1828) and Path Function (Routh 1881)
Conclusion

Exponential and Logarithmic Functions
Derivation Property, Series, and Rational Limit
Continued Fractions and Computation of the Number e
Transformation of Sums to Products and Powers
Limits, Period, and Absence of Zeros
Logarithm as the Function Inverse to Exponential
Series Expansions and Continued Fractions
Exponential and Logarithm with Complex Base
Tables of Natural (Napier 1614) and Decimal (Briggs 1624) Logarithms
Gaussian and Related Hypergeometric Functions
Conclusion

Plane Elasticity and Multiharmonic Functions
Displacement Vector and Deformation and Strain Tensors
Stress Vector, Tensor, and Function
Elastic Energy and Moduli of a Material (Hooke 1678; Poisson 1829a; Lamé 1852)
Momentum Equation for Isotropic Elasticity
Cavities and Static and Rotating Cylinders
Multiharmonic Equation and Fluid Loading on a Dam
Forces and Moments on a Wedge
Elastic Potential and Stresses in an Infinite Medium
Driven Loaded Wheel with Traction or Braking
Conclusion

Circular and Hyperbolic Functions
Sine/Cosine Representations on the Ellipse/Hyperbola
Secant, Cosecant, Tangent, and Cotangent
Formulas of Addition of Several Variables
Formulas for Multiple, Double, and Half Variable
Powers, Products, and Sums of the Functions
Chebychev (1859) Polynomials of Two Kinds
Orthogonal and Normalized Trigonometric Functions
Relations between Complex and Real Functions
Periods, Symmetries, Values, and Limits
Conclusion

Membranes, Capillarity, and Torsion
Linear and Nonlinear Deflection of a Membrane
Large Deflection of a Membrane by Weight or Pressure
Boundary Condition with Surface Tension
Wetting Angle and Capillary Rise
Warping, Stress, and Displacement Functions
Torsional Stiffness of a Multiply Connected Section
Hollow Elliptical or Thin or Cut Cross Sections
Torsion of Prisms with Triangular Cross Section (Saint-Venant 1885; Campos and Cunha 2010)
Trajectories of Fluid Particles in a Rotating Vessel
Conclusion

Infinite and Cyclometric Representations
Power Series and Euler (1755)/Bernoulli (1713) Numbers
Branch Points and Branch Cuts for Cyclometric Functions
Derivatives/Primitives of Direct/Inverse Functions
Power Series for Cyclometric Functions
Slopes at Zeros and Residues at Singularities
Series of Fractions for Meromorphic Functions
Relation with Factorization in Infinite Products
Continued Fractions for Direct/Inverse Functions
Gregory, Leibnitz, Brouncker, and Wallis Quadratures
Summary

Confined and Unsteady Flows
Cylinder Moving in Large Cavity
Two Cylinders in Relative Motion
Eccentric, Biconcave/Biconvex, and Semi-Recessed Cylinders
Ramp/Step in a Wall and Thick Pointed/Blunt Plate
Channel with Contraction/Expansion and a Thick Plate
Flat Plate with Partially Separated Flow
Airfoil with Plain/Slotted Flap/Slat
Flow Past Tandem Airfoils and Cascades
Instability of a Plane Vortex Sheet (Helmholtz 1868; Kelvin 1871)
Conclusion

Infinite Processes and Summability
Bounds for Integrals of Monotonic Functions
Genus of an Infinite Canonical Product (Weierstrass 1876)
Convergent and Periodic Continued Fractions
Derangement of Conditionally Convergent Series
Summation of Series of Rational Functions
Extension of Convergence to Summability (Euler 1755; Césaro 1890)
Cardinals of Enumerable, Continuum, and Discontinuous (Cantor 1874, 1878)
Transfinite Cardinal and Ordinal Numbers (Cantor 1883a,b; Hardy 1903)
Three Antinomies and the Axiom of Selection (Burali-Forti 1897; Russell 1903; Zermelo 1908)
Conclusion

Twenty Examples
Examples 10.1 through 10.20
Conclusion

Bibliography
Index

Über Autor(innen)

Luis Manuel Braga da Costa Campos is the director and founder of the Center for Aeronautical and Space Science and Technology at Lisbon Technical University, where he is also the coordinator of undergraduate and postgraduate degrees in aerospace engineering and coordinator of the applied and aerospace mechanics group in the Department of Mechanical Engineering. Dr. Campos is a member and vice chairman of the Portuguese Academy of Engineering; a fellow of the Royal Aeronautical Society, Astronomical Society, and Cambridge Philosophical Society; and associate fellow of the American Institute of Aeronautics and Astronautics. His research focuses on acoustics, magnetohydrodynamics, special functions, and flight dynamics.