目錄
CHAPTER I.KINEMATICS OF DEFORMABLE BGDIES
1.A Fundamental Theorem of Kinematics
2.Review of Vector Analysis
3.The Theorems of Gauss, Stokes, and Green
4.Some Remarks on Tensor Analysis
CHAPTER II.STATICS OF DEFORMABLE BODIES
5.Concept of Stress; General Classification of Deformable Bodies
6.Equilibrium of Incompressible Fluids (Hydrostatics)
7.Statics of Compressible Fluids
8.The State of Stress of an Elastic Solid
9.Strain-Stress Relations, Elastic Constants, Elastic Potential
10.Viscous Pressures and Dissipation, Particularly in Incompressible Fluids
CHAPTER III.DYNAMICS OF DEFORMABLE BODIES
11.Euler's Equations for a Perfect Incompressible Fluid
12.Derivation of Euler's Equations from Hamilton's Principle.The Pressure a Lagrange Multinliydwwsvsw
13.Euler's Equations for the Perfect Compressible Fluid and Their Application to Acoustics
Appendix.Comparison of Compressible and Incompressible Flows
14.Dynamics of the Elastic Body
15.The Quasi-Elastic Body as Model of the Ether
16.Dynamics of Viscous Fluids.Hydrodynamics and Hydraulics.Reynolds Criterion of Turbulence
17.Some Remarks on Capillarity
CHAPTER IV.VORTEX THEORY
18.Helmholtz's Vortex Theorems
1.The Differential Form of the Conservation Theorem
2.The Integral Form of the Conservation Theorem
3.The Spatial Distribution of the Vorticity
19.Two- and Three-dimensional Potential Flow
20.A Fundamental Theorem of Vector Analysis
21.Straight and Parallel Vortex Filaments
1.The Single Vortex Filament
2.Two Vortex Filaments of Equal Strength and Opposite or Equal Sense
3.A Theorem Concerning the "Center of Mass" of Two or More Vortices
4.The Law of Areas for a System of Vortex Filaments
5.General Remarks on the Dynamics of Vortices
6.Atmospheric Vortices
22.Circular Vortex Rings
CHAPTER V.THEORY OF WAVES
23.Plane Gravity Waves in Deep Water
24.Plane Gravity Waves in Shallow and Moderately Deep Water
25.Plane Capillary Waves and Combined Capillary-Gravity Waves
26.The Concept of Group Velocity
27.Circular Waves
1.The Periodic Case.Introduction of Bessel Functions
2.Single Disturbance.The Fourier-Bessel Integral
3.Integration with Respect to k.The Method of the Stationary Phase
4.Integration with Respect to a.Discussion of a Limiting Case
28.Ship Waves (Kelvin's Limit Angle and Mach's Angle)
CHAPTER VI.FLOW WITH GIVEN BOUNDARIES
29.Flow Past a Plate
30.The Problem of the Wake; Surfaces of Discontinuity
31.The Problem of the Free Jet Solved by Conformal Mapping
32.K?rm?n's Vortex Street Appendix.The Drag Problem
33.Prandtl's Boundary Layer
CHAPTER VII.SUPPLEMENTARY NOTES ON SELECTED HYDRODYNAMIC PROBLEMS
34.Lagrange's Equations of Motion
35.Stokes'Resistance Law
36.The Hydrodynamic Theory of Lubrication
37.Riemann's Shock Waves.General Integration of Euler's Equations for a Compressible Fluid in One-dimensional Flow
38.On Turbulence
A.Some Properties of Turbulent Flow
B.Older Attempts at a Mathematical Theory of Reynolds' Turbulence Criterion
C.Reformulation of the Turbulence Problem; the Origin of the Turbu- lence
D.The Limiting Case of Isotropic Turbulence
E.A Mathematical Model to Illustrate the Turbulence Problem
CHAPTER VIII.SUPPLEMENTS TO THE THEORY OF ELASTICITY
39.Elastic Limit, Proportional Limit, Yield Point, Plasticity, and Strength
40.Crystal Elasticity
41.The Bending of Beams
42.Torsion
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