Mechanics of Deformable Bodies

Mechanics of Deformable Bodies

Lectures on Theoretical Physics

1st Edition - January 1, 1950

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  • Author: Arnold Sommerfeld
  • eBook ISBN: 9781483220277

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Description

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.

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 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

    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. Karman'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 Isotropic Turbulence

    E. A Mathematical Model to Illustrate the Turbulence Problem

    Chapter VIII. Supplements To The Theory Op 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: 9781483220277

About the Author

Arnold Sommerfeld

Affiliations and Expertise

University of Munich

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