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Introduction to Classical Mechanics

Book Description

This textbook covers all the standard introductory topics in classical mechanics, including Newton's laws, oscillations, energy, momentum, angular momentum, planetary motion, and special relativity. It also explores more advanced topics, such as normal modes, the Lagrangian method, gyroscopic motion, fictitious forces, 4-vectors, and general relativity. It contains more than 250 problems with detailed solutions so students can easily check their understanding of the topic. There are also over 350 unworked exercises which are ideal for homework assignments. Password protected solutions are available to instructors at www.cambridge.org/9780521876223. The vast number of problems alone makes it an ideal supplementary text for all levels of undergraduate physics courses in classical mechanics. Remarks are scattered throughout the text, discussing issues that are often glossed over in other textbooks, and it is thoroughly illustrated with more than 600 figures to help demonstrate key concepts.

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright Page
  4. Dedication
  5. Contents
  6. Preface
  7. Chapter 1: Strategies for solving problems
    1. 1.1 General strategies
    2. 1.2 Units, dimensional analysis
    3. 1.3 Approximations, limiting cases
    4. 1.4 Solving differential equations numerically
    5. 1.5 Problems
    6. 1.6 Exercises
    7. 1.7 Solutions
  8. Chapter 2: Statics
    1. 2.1 Balancing forces
    2. 2.2 Balancing torques
    3. 2.3 Problems
    4. 2.4 Exercises
    5. 2.5 Solutions
  9. Chapter 3: Using F = ma
    1. 3.1 Newton’s laws
    2. 3.2 Free-body diagrams
    3. 3.3 Solving differential equations
    4. 3.4 Projectile motion
    5. 3.5 Motion in a plane, polar coordinates
    6. 3.6 Problems
    7. 3.7 Exercises
    8. 3.8 Solutions
  10. Chapter 4: Oscillations
    1. 4.1 Linear differential equations
    2. 4.2 Simple harmonic motion
    3. 4.3 Damped harmonic motion
    4. 4.4 Driven (and damped) harmonic motion
    5. 4.5 Coupled oscillators
    6. 4.6 Problems
    7. 4.7 Exercises
    8. 4.8 Solutions
  11. Chapter 5: Conservation of energy and momentum
    1. 5.1 Conservation of energy in one dimension
    2. 5.2 Small oscillations
    3. 5.3 Conservation of energy in three dimensions
    4. 5.4 Gravity
    5. 5.5 Momentum
    6. 5.6 The center of mass frame
    7. 5.7 Collisions
    8. 5.8 Inherently inelastic processes
    9. 5.9 Problems
    10. 5.10 Exercises
    11. 5.11 Solutions
  12. Chapter 6: The Lagrangian method
    1. 6.1 The Euler–Lagrange equations
    2. 6.2 The principle of stationary action
    3. 6.3 Forces of constraint
    4. 6.4 Change of coordinates
    5. 6.5 Conservation laws
    6. 6.6 Noether’s theorem
    7. 6.7 Small oscillations
    8. 6.8 Other applications
    9. 6.9 Problems
    10. 6.10 Exercises
    11. 6.11 Solutions
  13. Chapter 7: Central forces
    1. 7.1 Conservation of angular momentum
    2. 7.2 The effective potential
    3. 7.3 Solving the equations of motion
    4. 7.4 Gravity, Kepler’s laws
    5. 7.5 Problems
    6. 7.6 Exercises
    7. 7.7 Solutions
  14. Chapter 8: Angular momentum, Part I (Constant L)
    1. 8.1 Pancake object in x-y plane
    2. 8.2 Nonplanar objects
    3. 8.3 Calculating moments of inertia
    4. 8.4 Torque
    5. 8.5 Collisions
    6. 8.6 Angular impulse
    7. 8.7 Problems
    8. 8.8 Exercises
    9. 8.9 Solutions
  15. Chapter 9: Angular momentum, Part II (General L)
    1. 9.1 Preliminaries concerning rotations
    2. 9.2 The inertia tensor
    3. 9.3 Principal axes
    4. 9.4 Two basic types of problems
    5. 9.5 Euler’s equations
    6. 9.6 Free symmetric top
    7. 9.7 Heavy symmetric top
    8. 9.8 Problems
    9. 9.9 Exercises
    10. 9.10 Solutions
  16. Chapter 10: Accelerating frames of reference
    1. 10.1 Relating the coordinates
    2. 10.2 The fictitious forces
    3. 10.3 Tides
    4. 10.4 Problems
    5. 10.5 Exercises
    6. 10.6 Solutions
  17. Chapter 11: Relativity (Kinematics)
    1. 11.1 Motivation
    2. 11.2 The postulates
    3. 11.3 The fundamental effects
    4. 11.4 The Lorentz transformations
    5. 11.5 Velocity addition
    6. 11.6 The invariant interval
    7. 11.7 Minkowski diagrams
    8. 11.8 The Doppler effect
    9. 11.9 Rapidity
    10. 11.10 Relativity without c
    11. 11.11 Problems
    12. 11.12 Exercises
    13. 11.13 Solutions
  18. Chapter 12: Relativity (Dynamics)
    1. 12.1 Energy and momentum
    2. 12.2 Transformations of E and p
    3. 12.3 Collisions and decays
    4. 12.4 Particle-physics units
    5. 12.5 Force
    6. 12.6 Rocket motion
    7. 12.7 Relativistic strings
    8. 12.8 Problems
    9. 12.9 Exercises
    10. 12.10 Solutions
  19. Chapter 13: 4-vectors
    1. 13.1 Definition of 4-vectors
    2. 13.2 Examples of 4-vectors
    3. 13.3 Properties of 4-vectors
    4. 13.4 Energy, momentum
    5. 13.5 Force and acceleration
    6. 13.6 The form of physical laws
    7. 13.7 Problems
    8. 13.8 Exercises
    9. 13.9 Solutions
  20. 14 General Relativity
    1. 14.1 The Equivalence Principle
    2. 14.2 Time dilation
    3. 14.3 Uniformly accelerating frame
    4. 14.4 Maximal-proper-time principle
    5. 14.5 Twin paradox revisited
    6. 14.6 Problems
    7. 14.7 Exercises
    8. 14.8 Solutions
  21. Appendix A Useful formulas
  22. Appendix B Multivariable, vector calculus
  23. Appendix C F = ma vs. F = dp/dt
  24. Appendix D Existence of principal axes
  25. Appendix E Diagonalizing matrices
  26. Appendix F Qualitative relativity questions
  27. Appendix G Derivations of the Lv/c2 result
  28. Appendix H Resolutions to the twin paradox
  29. Appendix I Lorentz transformations
  30. Appendix J Physical constants and data
  31. References
  32. Index