Sommerfeld Mechanics of Deformable Bodies

Lectures on Theoretical Physics
1. Auflage 2013
ISBN: 978-1-4832-2027-7
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 408 Seiten, Web PDF

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.

Autoren/Hrsg.

Sommerfeld, Arnold

Inhaltsverzeichnis

1;Front Cover;1
2;Mechanics of Deformable Bodies: Lectures on Theoretical Physics;4
3;Copyright Page;5
4;Table of Contents;10
5;PREFACE;6
6;CHAPTER I. KINEMATICS OF DEFORMABLE BODIES;14
6.1;1. A Fundamental Theorem of Kinematics;14
6.2;2. Review of Vector Analysis;22
6.3;3. The Theorems of Gauss, Stokes, and Green;32
6.4;4. Some Remarks on Tensor Analysis;39
7;CHAPTER II. STATICS OF DEFORMABLE BODIES;50
7.1;5. Concept of Stress; General Classification of Deformable Bodies;50
7.2;6. Equilibrium of Incompressible Fluids (Hydrostatics);54
7.3;7. Statics of Compressible Fluids;62
7.4;8. The State of Stress of an Elastic Solid;68
7.5;9. Strain-Stress Relations, Elastic Constants, Elastic Potential;74
7.6;10. Viscous Pressures and Dissipation, Particularly in Incompressible Fluids;86
8;CHAPTER III. DYNAMICS OF DEFORMABLE BODIES;96
8.1;11. Euler's Equations for a Perfect Incompressible Fluid;96
8.2;12. Derivation of Euler's Equations from Hamilton's Principle The Pressure, a Lagrange Multiplier;102
8.3;13. Euler's Equations for the Perfect Compressible Fluid and Their Application to Acoustics;107
8.4;Appendix;114
8.5;14. Dynamics of the Elastic Body;118
8.6;15. The Quasi-Elastic Body as Model of the Ether;121
8.7;16. Dynamics of Viscous Fluids. Hydrodynamics and Hydraulics. Reynolds' Criterion of Turbulence;126
8.8;17. Some Remarks on Capillarity;135
9;CHAPTER IV. VORTEX THEORY;142
9.1;18. Helmholtz's Vortex Theorems;142
9.2;19. Two- and Three-dimensional Potential Flow;150
9.3;20. A Fundamental Theorem of Vector Analysis;160
9.4;21. Straight and Parallel Vortex Filaments;167
9.5;22. Circular Vortex Rings;174
10;CHAPTER V. THEORY OF WAVES;181
10.1;23. Plane Gravity Waves in Deep Water;181
10.2;24. Plane Gravity Waves in Shallow and Moderately Deep Water;186
10.3;25. Plane Capillary Waves and Combined Capillary-Gravity Waves;193
10.4;26. The Concept of Group Velocity;197
10.5;27. Circular Waves;204
10.6;28. Ship Waves (Kelvin's Limit Angle and Mach's Angle);213
11;CHAPTER VI. FLOW WITH GIVEN BOUNDARIES;220
11.1;29. Flow Past a Plate;220
11.2;30. The Problem of the Wake; Surfaces of Discontinuity;228
11.3;31. The Problem of the Free Jet Solved by Conformed Mapping;237
11.4;32. Kármán's Vortex Street;244
11.5;Appendix The Drag Problem;252
11.6;33. Prandtl's Boundary Layer;254
12;CHAPTER VIII. SUPPLEMENTARY NOTES ON SELECTED HYDRODYNAMIC PROBLEMS;257
12.1;34. Lagrange's Equations of Motion;257
12.2;35. Stokes's Resistance Law;259
12.3;36. The Hydrodynamic Theory of Lubrication;266
12.4;37. Riemann's Shock Waves. General Integration of Euler's Equa-tions for a Compressible Fluid in One-dimensional Flow;275
12.5;38. On Turbulence;284
13;CHAPTER VIII. SUPPLEMENTS TO THE THEORY OF ELASTICITY;298
13.1;39. Elastic Limit, Proportional Limit, Yield Point, Plasticity, and Strength;298
13.2;40. Crystal Elasticity;301
13.3;41. The Bending of Beams;306
13.4;42. Torsion;313
13.5;43. Torsion and Bending of a Helical Spring;321
13.6;44. The Elastic Energy Content of a Rectangular Parallelepiped;327
13.7;45. The Surface Waves of the Elastic Half-Space;339
13.8;PROBLEMS;349
14;ANSWERS AND COMMENTS;358
15;APPENDIX;393
15.1;APPENDIX I: THE COMPONENTS OF THE THREE-DIMENSIONAL STRAIN TENSOR IN ORTHOGONAL CURVILINEAR COORDINATES;393
15.2;APPENDIX II: THE CONVECTIVE TERMS OF THE ACCELERATION VECTOR IN TENSOR NOTATION;396
15.3;APPENDIX III: THE TENSOR OF FRICTION PRESSURES AND ITS DIVERGENCE;398
15.4;APPENDIX IV: THE EQUATIONS OF MOTION OF A VISCOUS INCOMPRESSIBLE FLUID IN CYLINDRICAL AND SPHERICAL COORDINATES;401
16;INDEX;404