Classical Mechanics 2nd Edition

by Corben, H.C.; Stehle, Philip

• ISBN13: 9780486680637
• ISBN10: 0486680630
• eBook ISBN(s): 9780486140780
• Edition: 2nd
• Format: Paperback
• Copyright: 1994-08-18
• Publisher: Dover Publications
• More Book Details
• Purchase Benefits

Summary

Graduate-level text. Kinematics of particles, laws of motion, rigid bodies, relativity theory, much more. Exercises. References.

Table of Contents

Chapter 1. Kinematics of Particles
1. Introduction
2. Definition and Description of Particles
3. Velocity
4. Acceleration
5. Special Coordinate Systems
6. Vector Algebra
7. Kinematics and Measurement
  Exercises
Chapter 2. The Laws of Motion
8. Mass
9. Momentum and Force
10. Kinetic Energy
11. Potential Energy
12. Conservation of Energy
13. Angular Momentum
14. Rigid Body Rotating about a Fixed Point
15. A Theorem on Quadratic Functions
16. Inertial and Gravitational Masses
  Exercises
Chapter 3. Conservative Systems with One Degree of Freedom
17. The Oscillator
18. The Plan Pendulum
19. Child-Langmuir Law
  Exercises
Chapter 4. Two-Particle Systems
20. Introduction
21. Reduced Mass
22. Relative Kinetic Energy
23. Laboratory and Center-of-Mass Systems
24. Central Motion
  Exercises
Chapter 5. Time-Dependent Forces and Nonconservative Motion
25. Introduction
26. The Inverted Pedulum
27. Rocket Motion
28. Atmospheric Drag
29. The Poynting-Robertson Effect
30. The Damped Oscillator
  Exercises
Chapter 6. Lagrange's Equations of Motion
31. Derivation of Lagrange's Equations
32. The Lagrangian Function
33. The Jacobian Integral
34. Momentum Integrals
35. Charged Particle in an Electromagnetic Field
  Exercises
Chapter 7. Applications of Lagrange's Equations
36. Orbits under a Central Force
37. Kepler Motion
38. Rutherford Scattering
39. The Spherical Pendulum
40. Larmor's Theorem
41. The Cylindrical Magnetron
  Exercises
Chapter 8. Small Oscillations
42. Oscillations of a Natural System
43. Systems with Few Degrees of Freedom
44. "The Stretched String, Discrete Masses"
45. Reduction of the Number of Degrees of Freedom
46. Laplace Transforms and Dissipative Systems
  Exercises
Chapter 9. Rigid Bodies
47. Displacements of a Rigid Body
48. Euler's Angles
49. Kinematics of Rotation
50. The Momental Ellipsoid
51. The Free Rotator
52. Euler's Equations of Motion
  Exercises
Chapter 10. Hamiltonian Theory
53. Hamilton's Equations
54. Hamilton's Equations in Various Coordinate Systems
55. Charged Particle in an Electromagnetic Field
56. The Virial Theorem
57. Variational Principles
58. Contact Transformations
59. Alternative Forms of Contact Transformations
60. Alternative Forms of the Equations of Motion
  Exercises
Chapter 11. The Hamilton-Jacobi Method
61. The Hamilton-Jacobi Equation
62. Action and Angle Variables-Periodic Systems
63. Separable Mulitply-Periodic Systems
64. Applications
  Exercises
Chapter 12. Infinitesimal Contact Transformations
65. Transformation Theory of Classical Dynamics
66. Poisson Brackets
67. Jacobi's Identity
68. Poisson Brackets in Quantum Mechanics
  Exercises
Chapter 13. Further Development of Transformation Theory
69. Notation
70. Integral Invariants and Liouville's Theorem
71. Lagrange Brackets
72. Change of Independent Variable
73. Extended Contact Transformations
74. Perturbation Theroy
75. Stationary State Perturbation Theory
76. Time-Dependent Perturbation Theory
77. Quasi Coordinates and Quasi Momenta
  Exercises
Chapter 14. Special Applications
78. Noncentral Forces
79. Spin Motion
80. Variational Principles in Rocket Motion
81. The Boltzmann and Navier-Stokes Equations
Chapter 15. Continuous Media and Fields
82. The Stretched String
83. Energy-Momentum Relations
84. Three-Dimensional Media and Fields
85. Hamiltonian Form of Field Theory
  Exercises
Chapter 16. Introduction to Special Relativity Theory
86. Introduction
87. Space-Time and Lorentz Transformation
88. The Motion of a Free Particle
89. Charged Particle in an Electromagnetic Field
90. Hamiltonian Formulation of the Equations of Motion
91. Transformation Theory and the Lorentz Group
92. Thomas Precession
  Exercises
Chapter 17. The Orbits of Particles in High Energy Accelerators
93. Introduction
94. Equilibrium Orbits
95. Betatron Oscillations
96. Weak Focusing Accelerators
97. Strong Focusing Accelerators
98. Acceleration and Synchrotron Oscillations
Appendix I Riemannian Geometry
Appendix II Linear Vector Spaces
Appendix III Group Theory and Molecular Vibrations
Apendix IV Quaternions and Pauli Spin Matrices
Index