01/04

Logistical
Information. Motivation. Why Classical
Mechanics?
What is Classical Mechanics? Newton,
Lagrange, and Hamilton.
Basics: Time, Space, Frames, Mass,
Force.
Review: Newton's First Law. Newton's
Second Law. Newton's Third Law.

01/07 
Introduction to Calculus of
Variations: Shortest 2Segment Path
Between Points.
Shortest 3Segment Path Between Points.

01/09 
Shortest N+1Segment Path
Between Points. Example: A
Random Selection of Paths.
Intro: Shortest Smooth Path Between
Points.

01/11 
Shortest Smooth Path
Between Points. Functionals.
Calculus of Variations. General Functional
of a Single Function. EulerLagrange
Equations.

01/14 
Kinetic
Energy. Work. Conservative
Forces. Central Forces. Potential
Energy. Total Energy.
TimeDependent Potentials. Many Particle
Energetics: Total Kinetic Energy, Total
Potential Energy, Total Energy. Rigid
Bodies. The Virial Theorem 
01/16 
EulerLagrange
Equations. Example: The Brachistocrone
Problem.

01/18 
Finding
EulerLagrange when given a Functional.
Functionals of Many Functions. 
01/21 
Calculus
of Variations Applied to
Mechanics. The Lagrangian: A
Functional for Newton's Laws. Hamilton's
Principle of Least Action.
Lagrangian Mechanics. 
01/23 
Conservation
of Momentum.
Rocket
Propulsion. Video: Robert
Goddard Archival Footage. Video: SpaceX.
Example:Launching
a Rocket .
The Centre of Mass Coordinate.

01/25 
Lagrangian
Mechanics. The Pendulum.
Double Pendulum

01/28 
Worked
Solution: The Double Pendulum.
Quadratic Lagrangian.

01/30 
Normal
Modes of the Double Pendulum.
Example: Normal
Modes The Double Pendulum.

02/01 
Worked Solution: Two Masses
and Three Springs

02/04 
Point Grey Pendulum.
Ignorable Coordinates.
Noether's Theorem. 
02/06 
Noether's
Theorem. Translation Invariance:
Momentum Conservation. TimeTranslation
Invariance: Hamiltonian is Constant.
Atwood's Machine. Bead on a Rotating
Wire.

02/08 
Example: Bead on Rotating
Wire

02/11 
Group
Project Meetings / InClass: Springs in
Space 
02/13 
Group Project Meetings /
Kerbal Space Program

02/15 
Motion
of Two Particles under a Harmonic Force
Law (Springs in Space).
The
Effective Radial Potential for a 3D
Harmonic Oscillator. The TwoBody Problem in a
Central Potential. The General
Effective Potential for the TwoBody
Problem. Kepler Problem.

02/18
02/20
02/22

Reading Week No Classes

02/25 
TwoBody Central
Potential. Example: The Celestial
Two Body Problem. The Kepler
Problem. 
02/27

Midterm

03/01 
The
Kepler Problem: Solving the
Radial Equation.

03/04 
Worked
Example: Practice Midterm; Geometry
of Bound Solutions. Kepler's
Second and Third Law.

03/06 
Energy
in the Kepler Problem. Geometry
of Unbound Solutions.
Orbits
in the Kepler Problem,
Orbital Parameters. 
03/08 
Example:
Changes of Orbit,
Spaceship I 
03/11

Example: Gravity
Assist Maneuver

03/18 
Rotational Motion
of Rigid Bodies 
03/20 
Inertia Tensor,
Examples: Sphere About Centre,
Cylinder About Centre, Cone About
Pivot

03/25 
Euler Angles,
Principle Moments, Principle Axes.
Lagrangian for a Symmetric Top. 
03/27

Normal Modes K and
M Matrix Formalism

03/29

Hamiltonian
Mechanics

