Contents

• Introduction
  • Intended Audience
  • Major sources
  • Scope of Course
  • Outline of Course
  
  
• Vectors
  • Introduction
  • Vector Algebra
  • The Scalar Product
  • The Vector Product
  • Rotation
  • The Scalar Triple Product
  • The Vector Triple Product
  • Vector Calculus
  • Line Integrals
  • Vector Line Integrals
  • Gradient
  • Useful Vector Formulae
  • Exercises
  
  
• Fundamentals
  • Introduction
  • Fundamental Assumptions
  • Newton's Laws of Motion
  • Newton's First Law of Motion
  • Newton's Second Law of Motion
  • Newton's Third Law of Motion
  • Exercises
  
  
• One-Dimensional Motion
  • Introduction
  • Motion in a General One-Dimensional Potential
  • Velocity Dependent Forces
  • Simple Harmonic Motion
  • Damped Oscillatory Motion
  • Resonance
  • Periodic Driving Forces
  • Transients
  • The Simple Pendulum
  • Exercises
  
  
• Multi-Dimensional Motion
  • Introduction
  • Motion in a Two-Dimensional Harmonic Potential
  • Projectile Motion with Air Resistance
  • Motion in Crossed Electric and Magnetic Fields
  • Exercises
  
  
• Planetary Motion
  • Introduction
  • Kepler's Laws
  • Newtonian Gravity
  • Conservation Laws
  • Polar Coordinates
  • Conic Sections
  • Kepler's Second Law
  • Kepler's First Law
  • Kepler's Third Law
  • Orbital Energies
  • The Kepler Problem
  • Motion in a General Central Force-Field
  • Motion in a Nearly Circular Orbit
  • Exercises
  
  
• Two-Body Dynamics
  • Introduction
  • Reduced Mass
  • Binary Star Systems
  • Scattering in the Center of Mass Frame
  • Scattering in the Laboratory Frame
  • Exercises
  
  
• Non-Inertial Reference Frames
  • Introduction
  • Rotating Reference Frames
  • Centrifugal Acceleration
  • The Coriolis Force
  • The Foucault Pendulum
  • Exercises
  
  
• Rigid Body Motion
  • Introduction
  • Fundamental Equations
  • The Moment of Inertia Tensor
  • Rotational Kinetic Energy
  • Matrix Theory
  • The Principal Axes of Rotation
  • Euler's Equations
  • Eulerian Angles
  • Gyroscopic Precession
  • Rotational Stability
  • Exercises
  
  
• Lagrangian Dynamics
  • Introduction
  • Generalized Coordinates
  • Generalized Forces
  • Lagrange's Equation
  • Motion in a Central Potential
  • Atwood Machines
  • Sliding down a Sliding Plane
  • Generalized Momenta
  • The Spherical Pendulum
  • Exercises
  
  
• Hamiltonian Dynamics
  • Introduction
  • The Calculus of Variations
  • Conditional Variation
  • Multi-Function Variation
  • Hamilton's Principle
  • Constrained Lagrangian Dynamics
  • Hamilton's Equations
  • Exercises
  
  
• Coupled Oscillations
  • Introduction
  • Equilibrium State
  • Stability Equations
  • Mathematical Digression
  • Normal Modes
  • Normal Coordinates
  • Spring-Coupled Masses
  • Triatomic Molecule
  • Exercises
  
  
• Gravitational Potential Theory
  • Introduction
  • Gravitational Potential
  • Axially Symmetric Mass Distributions
  • Potential Due to a Uniform Sphere
  • Potential Outside a Uniform Spheroid
  • Rotational Flattening
  • McCullough's Formula
  • Tidal Elongation
  • Precession of the Equinoxes
  • Potential Due to a Uniform Ring
  • Perihelion Precession of the Planets
  • Perihelion Precession of Mercury
  • Exercises
  
  
• The Three-Body Problem
  • Introduction
  • The Circular Restricted Three-Body Problem
  • The Jacobi Integral
  • The Tisserand Criterion
  • The Co-Rotating Frame
  • The Lagrange Points
  • Zero-Velocity Surfaces
  • Stability of Lagrange Points
  
  
• The Chaotic Pendulum
  • Introduction
  • Analytic Solution
  • Numerical Solution
  • The Poincaré Section
  • Spatial Symmetry Breaking
  • Basins of Attraction
  • Period-Doubling Bifurcations
  • The Route to Chaos
  • Sensitivity to Initial Conditions
  • The Definition of Chaos
  • Periodic Windows
  • Further Investigation