Mechanics of Deformable Bodies

Mechanics of Deformable Bodies: Lectures on Theoretical Physics, Volume II covers topics on the mechanics of deformable bodies. The book discusses the kinematics, statics, and dynamics of deformable bodies; the vortex theory; as well as the theory of waves. The text also describes the flow with given boundaries. Supplementary notes on selected hydrodynamic problems and supplements to the theory of elasticity are provided. Physicists, mathematicians, and students taking related courses will find the book useful.

Contenu

Chapter I. Kinematics of Deformable Bodies

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 . 73
    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 Multiplier
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
19. The Differential Form of the Conservation Theorem
20. The Integral Form of the Conservation Theorem
21. The Spatial Distribution of the Vorticity
22. Two- and Three-dimensional Potential Flow
23. A Fundamental Theorem of Vector Analysis
24. Straight and Parallel Vortex Filaments
25. The Single Vortex Filament
26. Two Vortex Filaments of Equal Strength and Opposite or Equal Sense
27. A Theorem Concerning the "Center of Mass" of Two or More Vortices
28. The Law of Areas for a System of Vortex Filaments
29. General Remarks on the Dynamics of Vortices
30. Atmospheric Vortices
31. Circular Vortex Rings
    Chapter V. Theory of Waves
32. Plane Gravity Waves in Deep Water
33. Plane Gravity Waves in Shallow and Moderately Deep Water
34. Plane Capillary Waves and Combined Capillary-Gravity Waves
35. The Concept of Group Velocity
36. Circular Waves
37. The Periodic Case. Introduction of Bessel Functions
38. Single Disturbance. The Fourier-Bessel Integral
39. Integration with Respect to k. The Method of the Stationary Phase
40. Integration with Respect to a. Discussion of a Limiting Case
41. Ship Waves (Kelvin's Limit Angle and Mach's Angle)
    Chapter VI. Flow With Given Boundaries
42. Flow Past a Plate
43. The Problem of the Wake; Surfaces of Discontinuity
44. The Problem of the Free Jet Solved by Conformal Mapping
45. Karman's Vortex Street
    Appendix. The Drag Problem
46. Prandtl's Boundary Layer
    Chapter VII. Supplementary Notes On Selected Hydrodynamic Problems
47. Lagrange's Equations of Motion
48. Stokes' Resistance Law
49. The Hydrodynamic Theory of Lubrication
50. Riemann's Shock Waves. General Integration of Euler's Equations for a Compressible Fluid in One-dimensional Flow
51. 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 Turbulence
    D. The Limiting Case of Isotropic Turbulence
    E. A Mathematical Model to Illustrate the Turbulence Problem
    Chapter VIII. Supplements To The Theory Op Elasticity
52. Elastic Limit, Proportional Limit, Yield Point, Plasticity, and Strength
53. Crystal Elasticity
54. The Bending of Beams
55. Torsion
56. Torsion and Bending of a Helical Spring
57. The Elastic Energy Content of a Rectangular Parallelepiped
58. The Surface Waves of the Elastic Half-Space
    A. Reflection of a Plane Transverse Spatial Wave
    B. Elastic Surface Waves
    Problems
    Chapter I
    Chapter II
    Chapter III
    Chapter IV
    Chapters V and VI
    Chapter VII
    Chapter VIII
    Answers and Comments
    Appendix I
    Appendix II
    Appendix III
    Appendix IV
    Index