Mechanics of Deformable Bodies

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