Classical Mechanics (eBook)

Chapter 1. Kinematics of Particles1. Introduction2. Definition and Description of Particles3. Velocity4. Acceleration5. Special Coordinate Systems6. Vector Algebra7. Kinematics and Measurement ExercisesChapter 2. The Laws of Motion8. Mass9. Momentum and Force10. Kinetic Energy11. Potential Energy12. Conservation of Energy13. Angular Momentum14. Rigid Body Rotating about a Fixed Point15. A Theorem on Quadratic Functions16. Inertial and Gravitational Masses ExercisesChapter 3. Conservative Systems with One Degree of Freedom17. The Oscillator18. The Plan Pendulum19. Child-Langmuir Law ExercisesChapter 4. Two-Particle Systems20. Introduction21. Reduced Mass22. Relative Kinetic Energy23. Laboratory and Center-of-Mass Systems24. Central Motion ExercisesChapter 5. Time-Dependent Forces and Nonconservative Motion25. Introduction26. The Inverted Pedulum27. Rocket Motion28. Atmospheric Drag29. The Poynting-Robertson Effect30. The Damped Oscillator ExercisesChapter 6. Lagrange's Equations of Motion31. Derivation of Lagrange's Equations32. The Lagrangian Function33. The Jacobian Integral34. Momentum Integrals35. Charged Particle in an Electromagnetic Field ExercisesChapter 7. Applications of Lagrange's Equations36. Orbits under a Central Force37. Kepler Motion38. Rutherford Scattering39. The Spherical Pendulum40. Larmor's Theorem41. The Cylindrical Magnetron ExercisesChapter 8. Small Oscillations42. Oscillations of a Natural System43. Systems with Few Degrees of Freedom44. "The Stretched String, Discrete Masses"45. Reduction of the Number of Degrees of Freedom46. Laplace Transforms and Dissipative Systems ExercisesChapter 9. Rigid Bodies47. Displacements of a Rigid Body48. Euler's Angles49. Kinematics of Rotation50. The Momental Ellipsoid51. The Free Rotator52. Euler's Equations of Motion ExercisesChapter 10. Hamiltonian Theory53. Hamilton's Equations54. Hamilton's Equations in Various Coordinate Systems55. Charged Particle in an Electromagnetic Field56. The Virial Theorem57. Variational Principles58. Contact Transformations59. Alternative Forms of Contact Transformations60. Alternative Forms of the Equations of Motion ExercisesChapter 11. The Hamilton-Jacobi Method61. The Hamilton-Jacobi Equation62. Action and Angle Variables-Periodic Systems63. Separable Mulitply-Periodic Systems64. Applications ExercisesChapter 12. Infinitesimal Contact Transformations 65. Transformation Theory of Classical Dynamics66. Poisson Brackets67. Jacobi's Identity68. Poisson Brackets in Quantum Mechanics ExercisesChapter 13. Further Development of Transformation Theory69. Notation70. Integral Invariants and Liouville's Theorem71. Lagrange Brackets72. Change of Independent Variable73. Extended Contact Transformations74. Perturbation Theroy75. Stationary State Perturbation Theory76. Time-Dependent Perturbation Theory77. Quasi Coordinates and Quasi Momenta ExercisesChapter 14. Special Applications78. Noncentral Forces79. Spin Motion80. Variational Principles in Rocket Motion81. The Boltzmann and Navier-Stokes EquationsChapter 15. Continuous Media and Fields82. The Stretched String83. Energy-Momentum Relations84. Three-Dimensional Media and Fields85. Hamiltonian Form of Field Theory ExercisesChapter 16. Introduction to Special Relativity Theory86. Introduction87. Space-Time and Lorentz Transformation88. The Motion of a Free Particle89. Charged Particle in an Electromagnetic Field90. Hamiltonian Formulation of the Equations of Motion91. Transformation Theory and the Lorentz Group92. Thomas Precession ExercisesChapter 17. The Orbits of Particles in High Energy Accelerators93. Introduction94. Equilibrium Orbits95. Betatron Oscillations96. Weak Focusing Accelerators97. Strong Focusing Accelerators98. Acceleration and Synchrotron OscillationsAppendix I Riemannian GeometryAppendix II Linear Vector SpacesAppendix III Group Theory and Molecular VibrationsApendix IV Quaternions and Pauli Spin MatricesIndex