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Contents
Contents
Mechanics
(UCSD Physics 110B)
January 1, 2009
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
