Lecture Notes from PHYS410 - Classical Mechanics, as taught by Dr. Steven Anlage in Spring, 2013. 

Lecture 1 (01/23/13): Introduction and Problem Solving
- Solving Problems Involving Newton's Laws of Motion
- Solving Problems Involving Conservation Laws
- Classical Mechanics

Lecture 2 (01/25/13): Newton's Laws of Motion
- Mass & Forces
- Newton's Laws of Motion for Point Particles
- Polar Coordinates

Lecture 3 (01/28/15): Polar Coordinates & Drag
- Polar Coordinates
- Motion of Objects Subject to Drag Force
- Linear Drag Force

Lecture 4 (01/30/15): Drag & Trajectories
- Linear Drag Force
- Quadratic Drag Force

Lecture 5 (02/01/13): Forces on Moving Charges
- Charge Moving in a Magnetic Field
- Motion in the xy-Plane

Lecture 6 (02/04/13): Motion Properties of Extended Objects
- Conservation of Linear Momentum for a Multi-Particle System
- Center of Mass
- Newton's 2nd Law for Extended Objects

Lecture 7 (02/06/13): Rotational Motion
- Angular Momentum
- Kepler's Law's of Motion
- Angular Momentum of Multi-Particle Systems
- Rigid-Body Motion

Lecture 8 (02/08/13): Energy
- Kinetic Energy
- Conservative Forces
- Non-Conservative Forces
- Associated Force

Lecture 9 (02/11/13): Energy Conservation in 1-Dimension
- Hooke's Law Restoring Force
- Classical Turning Points
- Equilibrium Points

Lecture 10 (02/13/13): Curvilinear Coordinate Systems
- Tangential Force
- Central Forces
- Spherically Symmetric Potentials

Lecture 11 (02/15/13): 2 Particle Interactions
- Potential Between Particles
- Energy for 2-Particle Systems
- Small Oscillations

Lecture 12 (02/18/13): Damped Simple Harmonic Motion
- LRC Circuit
- Decay Time
- Adding a Harmonic Driving Force

Lecture 13 (02/20/13): Oscillations Continued
- Driving Frequency
- Particular & Homogeneous (Undriven, Damped) Solutions
- Resonance

Lecture 14 (02/22/13): Motion in Non-Inertial Reference Frames
- Linear Acceleration
- Rotating Reference Frames
- Correction Forces

Lecture 15 (02/25/13): Physics in Rotating Reference Frames
- Coriolis Force
- Foucault Pendulum
- Movement of Energy in a Coupled Set

Lecture 16 (02/27/13): Foucault Pendulum Motion
- Coupled Coriolis Motion
- Special Cases
- Exam Review
-----------------END OF MIDTERM I MATERIAL-------------------------

Lecture 17 (03/04/13): Calculus of Variations
- Finding Extremum Values
- Euler-Lagrange Equation
- The Classical Path

Lecture 18 (03/08/13): Brachistochrone & Lagrangians
- The Brachistochrone Problem
- Lagrangians
- Classical Action

Lecture 19 (03/11/13): Advantages of Lagrangians
- Systems with Constraints
- Double Pendulum
- Degrees of Freedom
- Atwood Machine

Lecture 20 (03/13/13): Two Examples of Lagrangian Mechanics
- Infinite Cylinder
- Mass on Wedge
- Limit Checks

Lecture 21 (03/15/13): More on Lagrangians
- Bead on a Hoop
- Equilibrium Points
- Other Properties of Lagrangians

Lecture 22 (03/25/13): Two-Body Problem
- Center of Mass Reference
- Conservation of Angular Momentum
- Radial Equation

Lecture 23 (03/27/13): Two-Body Problem, con't
- Conservation of Energy
- Bounded & Unbounded Orbits

Lecture 24 (03/29/13): Orbits & Collisions
- Bounded Orbit
- Energy in the Orbit
- Collisions -> Scattering Theory
- 2D Density of Atoms
- Types of Scattering
- Scattering Cross-Section
- Hard Sphere Elastic Scattering

Lecture 25 (04/01/13): Rutherford Scattering
- Scattering Theory
- Rutherford Scattering
- Impulse-Momentum Theorem

Lecture 26 (04/03/13): Hamiltonian Dynamics
- Hamiltonian Dynamics
- Hamilton's Equations
- Quantum Mechanics Application
- Exam Review
-----------------END OF MIDTERM II MATERIAL------------------------

Lecture 27 (04/08/13): Phase Space Evolution
- Evolution of Phase Point
- 1D Harmonic Oscillator
- Multiple Systems

Lecture 28 (04/10/13): Liouville's Theorem
- Phase Space (q,p)
- 2n-Dimensional Space
- Liouville's Theorem
- Motion of Extended Objects

Lecture 29 (04/12/13): Rotation of Rigid Bodies
- Rotation of Rigid Bodies
- General Case: No Fixed Axis
- Principle Axes of Rotation
- Diagonalization of the Inertia Tensor

Lecture 30 (04/15/13): Rigid Body Rotation, con't
- Gyroscope
- Euler Equations for Rigid Body Rotation
- Top Precession

Lecture 31 (04/17/13): Euler's Equations for Rigid Body Rotation
- Euler's Equations with Zero Torque
- Stability of Rotation
- Coupled Oscillators

Lecture 32 (04/19/13): Coupled Oscillators
- Two Masses & Three Springs
- Normal Modes of Oscillation
- Normal Coordinates
- The Double Pendulum

Lecture 33 (04/22/13): Coupled Systems -> Small Oscillations
- Moment of Inertia Matrix
- Kuromoto Model

Lecture 34 (04/24/13): Coupled Oscillators & Non-Linear Mechanics
- N Oscillators
- Small Oscillation Approximation about a Stable Equilibrium
- Chaos and Nonlinear Mechanics

Lecture 35 (04/26/13): Nonlinear Mechanics & Chaos
- Linear vs. Nonlinear Systems
- Driven, Damped Pendulum
- Period-Doubling Cascade
- Chaos

Lecture 36 (04/29/13): Nonlinearity & Chaos, con't
- Rayleigh-Benard Convection
- Lyapunov Exponent
- Bifurcation

Lecture 37 (05/01/13): State Space Trajectories & Relativity
- Bifurcation Diagram
- The Poincare Section
- Hamiltonian Chaos
- Special Relativity
- Galilean Invariance
- Lorentz Invariance

Lecture 38 (05/03/13): Special Relativity
- Relativity of Time
- Length Contraction
- Lorentz Transformation
- Relativistic Velocity Addition

Lecture 39 (05/06/13): Relativistic Dynamics
- Lorentz Transformation
- 3D Rotations
- Scalar Lorentz Invariant

Lecture 40 (05/08/13): Relativistic Kinematics
- Relativistic Dynamics
- 4-Vectors