Classical Mechanics

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