Classical Mechanics

John R. Taylor
University of Colorado

RED material is the focus of our 2011 JHU Course

Contents

Part I: THE ESSENTIALS

  1. Newton's Laws of Motion
    1.1 Classical Mechanics
    1.2 Space and Time
    1.3 Mass and Force
    1.4 Newton's First and Second Laws; Inertial Frames
    1.5 The Third Law and Conservation of the Momentum
    1.6 Newton's Second Law in Cartesian Coordinates
    1.7 Two-Dimensional Polar Coordinates
    1.8 Problems for Chapter 1

  2. Projectiles and Charged Particles
    2.1 Air Resistance
    2.2 Linear Air Resistance
    2.3 Trajectory and Range in a Linear Motion
    2.4 Quadratic Air Resistance
    2.5 Motion of a Charge in a Uniform Magnetic Field
    2.6 Complex Exponentials
    2.7 Solution for the Charge in a B Field
    2.8 Problems for Chapter 2

  3. Momentum and Angular Momentum
    3.1 Conservation of Momentum
    3.2 Rockets
    3.3 The Center of Mass
    3.4 Angular Momentum for a Single Particle
    3.5 Angular Momentum for Several Particles
    3.6 Problems for Chapter 3

  4. Energy
    4.1 Kinetic Energy and Work
    4.2 Potential Energy and Conservative Forces
    4.3 Force as the Gradient of Potential Energy
    4.4 The Second Condition that F be Conservative
    4.5 Time-Dependent Potential Energy
    4.6 Energy for Linear One-Dimensional Systems
    4.7 Curvilinear One-Dimensional Systems
    4.8 Central Forces
    4.9 Energy of Interaction of Two Particles
    4.10 The Energy of a Multiparticle System
    4.11 Problems for Chapter 4

  5. Oscillations
    5.1 Hooke's Law
    5.2 Simple Harmonic Motion
    5.3 Two-Dimensional Oscillators
    5.4 Damped Oscillators
    5.5 Driven Damped Oscillations
    5.6 Resonance
    5.7 Fourier Series
    5.8 Fourier Series Solution for the Driven Oscillator
    5.9 The RMS Displacement; Parseval's Theorem
    5.10 Problems for Chapter 5

  6. Calculus of Variations
    6.1 Two Examples
    6.2 The Euler-Lagrange Equation
    6.3 Applications of the Euler-Lagrange Equation
    6.4 More than Two Variables
    6.5 Problems for Chapter 6

  7. Lagrange's Equations
    7.1 Lagrange's Equations for Unconstrained Motion
    7.2 Constrained Systems; an Example
    7.3 Constrained Systems in General
    7.4 Proof of Lagrange's Equations with Constraints
    7.5 Examples of Lagrange's Equations
    7.6 Conclusion
    7.7 Conservation Laws in Lagrangian Mechanics
    7.8 Lagrange's Equations for Magnetic Forces
    7.9 Lagrange Multipliers and Constraint Forces
    7.10 Problems for Chapter 7

  8. Two-Body Central Force Problems
    8.1 The Problem
    8.2 CM and Relative Coordinates; Reduced Mass
    8.3 The Equations of Motion
    8.4 The Equivalent One-Dimensional Problems
    8.5 The Equation of the Orbit
    8.6 The Kepler Orbits
    8.7 The Unbonded Kepler Orbits
    8.8 Changes of Orbit
    8.9 Problems for Chapter 8

  9. Mechanics in Noninertial Frames
    9.1 Acceleration without Rotation
    9.2 The Tides
    9.3 The Angular Velocity Vector
    9.4 Time Derivatives in a Rotating Frame
    9.5 Newton's Second Law in a Rotating Frame
    9.6 The Centrifugal Force
    9.7 The Coriolis Force
    9.8 Free Fall and The Coriolis Force
    9.9 The Foucault Pendulum
    9.10 Coriolis Force and Coriolis Acceleration
    9.11 Problems for Chapter 9

  10. Motion of Rigid Bodies
    10.1 Properties of the Center of Mass
    10.2 Rotation about a Fixed Axis
    10.3 Rotation about Any Axis; the Inertia Tensor
    10.4 Principal Axes of Inertia
    10.5 Finding the Principal Axes; Eigenvalue Equations
    10.6 Precession of a Top Due to a Weak Torque
    10.7 Euler's Equations
    10.8 Euler's Equations with Zero Torque
    1
    0.9 Euler Angles
    10.10 Motion of a Spinning Top

    10.11 Problems for Chapter 10

  11. Coupled Oscillators and Normal Modes
    11.1 Two Masses and Three Springs
    11.2 Identical Springs and Equal Masses
    11.3 Two Weakly Coupled Oscillators
    11.4 Lagrangian Approach; the Double Pendulum
    11.5 The General Case
    11.6 Three Coupled Pendulums
    11.7 Normal Coordinates
    11.8 Problems for Chapter 11

    Part II: FURTHER TOPICS

  12. Nonlinear Mechanics and Chaos
    12.1 Linearity and Nonlinearity
    12.2 The Driven Damped Pendulum or DDP
    12.3 Some Expected Features of the DDP
    12.4 The DDP; Approach to Chaos
    12.5 Chaos and Sensitivity to Initial Conditions
    12.6 Bifurcation Diagrams
    12.7 State-Space Orbits
    12.8 Poincare Sections
    12.9 The Logistic Map
    12.10 Problems for Chapter 12

  13. Hamiltonian Mechanics
    13.1 The Basic Variables
    13.2 Hamilton's Equations for One-Dimensional Systems
    13.3 Hamilton's Equations in Several Dimensions
    13.4 Ignorable Coordinates
    13.5 Lagrange's Equations vs. Hamilton's Equations
    13.6 Phase-Space Orbits
    13.7 Liouville's Theorem
    13.8 Problems for Chapter 13

  14. Collision Theory
    14.1 The Scattering Angle and Impact Parameter
    14.2 The Collision Cross Section
    14.3 Generalizations of the Cross Section
    14.4 The Differential Scattering Cross Section
    14.5 Calculating the Differential Cross Section
    14.6 Rutherford Scattering
    14.7 Cross Sections in Various Frames
    14.8 Relation of the CM and Lab Scattering Angles
    14.9 Problems for Chapter 14

  15. Special Relativity
    15.1 Relativity
    15.2 Galilean Relativity
    15.3 The Postulates of Special Relativity
    15.4 The Relativity of Time; Time Dilation
    15.5 Length Contraction
    15.6 The Lorentz Transformation
    15.7 The Relativistic Velocity-Addition Formula
    15.8 Four-Dimensional Space-Time; Four-Vectors
    15.9 The Invariant Scalar Product
    15.10 The Light Cone
    15.11 The Quotient Rule and Doppler Effect
    15.12 Mass, Four-Velocity, and Four-Momentum
    15.13 Energy, the Fourth Component of Momentum
    15.14 Collisions
    15.15 Force in Relativity
    15.16 Massless Particles; the Photon
    15.17 Tensors
    15.18 Electrodynamics and Relativity
    15.19 Problems for Chapters 15
     

  16. Continuum Mechanics
    16.1 Transverse Motion of a Taut String
    16.2 The Wave Equation
    16.3  Boundary Conditions; Waves on a Finite String
    16.4 The Three-Dimensional Wave Equation
    16.5 Volume and Surface Forces
    16.6 Stress and Strain: the Elastic Moduli
    16.7 The Stress Tensor
    16.8 The Strain Tensor for a Solid
    16.9 Relation between Stress and Strain: Hooke's Law
    16.10 The Equation of Motion for an Elastic Solid
    16.11 Longitudinal and Transverse Waves in a Solid
    16.12 Fluids: Description of the Motion
    16.13 Waves in a Fluid
    16.14 Problems for Chapter 16

Appendix: Diagonalizing Real Symmetric Matrices

Further Reading

Answers for Odd-Numbered Problems

Index