Contents

• Vectors and Rotations
  • Vector Identities
  • Cross Products and Axial Vectors
  • Rotations
  • The Vector Derivative $\vec{\nabla}$
  • Homework Problems
  
  
• Noninertial Frames of Reference
  • Rotating Coordinate System
  • Calculating the Effective Force (a more general derivation)
  • Motion Near the Earth
  • The Tides
  • Homework Problems
  
  
• Dynamics of Rigid Bodies
  • Calculating the Kinetic Energy
  • The Inertia Tensor
  • Parallel Axis Theorem
  • Example: The Inertia Tensor for a Cube
  • Principal Axes
  • Euler Angles
  • Body Frame Coordinates
  • Euler's Equations
  • Stability of Rigid Body Rotations
  • Lagrange Equations for Top with One Fixed Point
  • Homework
  
  
• Special Relativity
  • Some History of Special Relativity
  • The Michelson Morley Experiment: Some Analysis
  • The Lorentz Transformation
  • Checking Michelson Morley with Lorentz Transformation
  • Minkowski Space
  • Causality and the Light Cone
  • Symmetry Transformations in Minkowski Space
  • Review of the Hyperbolic Functions
  • ``Rotations'' in 4 Dimensions
  • Velocity Addition
  • The Momentum-Energy 4-Vector
  • Summary of 4-Vectors
  • The 4D Gradient Operator ${\partial\over \partial x_\mu}$
  • The Relativistic Doppler Effect
  • The Twin Paradox
  • Kinematics Problems in Electron Volts
  • Lagrange Equations in Special Relativity
  • Covariant Electricity and Magnetism Equations
  • E&M is a Vector Theory
  • Homework
  
  
• A Little General Relativity
  • Geometries
  • The Metric Tensor
  • The Schwarzschild Metric
  • Gravity's Effect on Time and the Gravitational Red Shift
  • The Singularity in Schwarzschild Coordinates
  • The Geodesic Equation
  • Conserved Energy and Angular Momentum in the Schwarzschild Metric
  • Orbits in the Schwarzschild Metric
  • Orbits of Photons
  • Black Holes
  • Homework
  
  
• Hamiltonian Mechanics
  • Recalling Lagrangian Mechanics
  • The Hamiltonian Formalism
  • Conserved Momenta
  • Simple Example: Particle on the Surface of a Cylinder
  • Example: Particle in 3D Potential $V(x,y,z)$
  • Example: A spherical pendulum
  • Example: Motion in a Central Potential $V(r)$
  • Phase Space and Liouville's Theorem
  • Homework
  
  
• Continuum Mechanics
  • Homework