Courses of Mechanics

(UCSD Physics 110B)

• Contents
• Vectors and Rotations
  • Vector Identities
  • Cross Products and Axial Vectors
  • Rotations
  • The Vector Derivative 
  • Homework Problems
• Noninertial Frames of Reference
  • Rotating Coordinate System
    • Calculating the Effective Force (simple rotation)
  • Calculating the Effective Force (a more general derivation)
  • Motion Near the Earth
  • The Tides
    • Example: Deflection of a Falling Object
    • Example: Deflection of Cannon Balls
    • Weather Systems
    • Example: The Foucault Pendulum
  • Homework Problems
• Dynamics of Rigid Bodies
  • Calculating the Kinetic Energy
  • The Inertia Tensor
    • Angular Momentum
    • Simple Example: Inertia Tensor for Dumbbell
    • Transforming the Inertia Tensor
  • Parallel Axis Theorem
  • Example: The Inertia Tensor for a Cube
  • Principal Axes
    • Example: Cube Rotating about a Corner
    • Proof: Principal Axes Orthogonal
    • Proof: Roots  are Real
  • Euler Angles
  • Body Frame Coordinates
  • Euler's Equations
    • Example: Symmetric Top with no Torque
  • 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
    • Phenomena of the Lorentz Transformation
  • Minkowski Space
    • Proper Time
  • Causality and the Light Cone
  • Symmetry Transformations in Minkowski Space
  • Review of the Hyperbolic Functions
    • Hyperbolic Function Identities
  • ``Rotations'' in 4 Dimensions
    • Imaginary Angles
    • A Boost in an Arbitrary Direction
  • Velocity Addition
  • The Momentum-Energy 4-Vector
    • Deriving the Momentum-Energy 4-Vector
    • The Force 4-Vector
  • Summary of 4-Vectors
  • The 4D Gradient Operator 
  • The Relativistic Doppler Effect
  • The Twin Paradox
  • Kinematics Problems in Electron Volts
    •  Decay
    • Neutron Decay
    • Compton Scattering
  • Lagrange Equations in Special Relativity
  • Covariant Electricity and Magnetism Equations
    • Rationalized Heaviside-Lorentz Units
    • The Electromagnetic Field Tensor
    • Lorentz Transformation of the Fields
  • 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
    • Deflection of Light
  • 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 
  • Example: A spherical pendulum
  • Example: Motion in a Central Potential 
  • Phase Space and Liouville's Theorem
  • Homework
• Continuum Mechanics
  • Homework
• About this document ...

Jim Branson 2012-10-21