Mechanics of Deformable Bodies
Lectures on Theoretical Physics, Vol. 2
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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 test also describes flow with given boundaries. Supplementary notes on selected hydrodynamic problems, as well as supplements to the theory of elasticity are also provided. Physicists, mathematicians, and students taking related courses will find the book invaluable.
Table of Contents
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 Deformabile 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 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
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 194
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 Conformai Mapping
32. Kârmân'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 Turbulence
D. The Limiting Case of Isotropie 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
43. Torsion and Bending of a Helical Spring
44. The Elastic Energy Content of a Rectangular Parallelepiped
45. 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
Product details
- No. of pages: 408
- Language: English
- Copyright: © Academic Press 1950
- Published: January 1, 1950
- Imprint: Academic Press
- eBook ISBN: 9781483214283
About the Author
Arnold Sommerfeld
Affiliations and Expertise
University of Munich
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