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Vectors and Rotations
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Classical Mechanics 110B
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Classical Mechanics 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 (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
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
Example: A spherical pendulum
Example: Motion in a Central Potential
Phase Space and Liouville's Theorem
Homework
Continuum Mechanics
Homework
Jim Branson 2012-10-21