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 2-Segment Path
Between Points.
Shortest 3-Segment Path Between Points.
|
| 01/09 |
Shortest N+1-Segment 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. Euler-Lagrange
Equations.
|
| 01/14 |
Kinetic
Energy. Work. Conservative
Forces. Central Forces. Potential
Energy. Total Energy.
Time-Dependent Potentials. Many Particle
Energetics: Total Kinetic Energy, Total
Potential Energy, Total Energy. Rigid
Bodies. The Virial Theorem |
| 01/16 |
Euler-Lagrange
Equations. Example: The Brachistocrone
Problem.
|
| 01/18 |
Finding
Euler-Lagrange 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. Time-Translation
Invariance: Hamiltonian is Constant.
Atwood's Machine. Bead on a Rotating
Wire.
|
| 02/08 |
Example: Bead on Rotating
Wire
|
| 02/11 |
Group
Project Meetings / In-Class: 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 Two-Body Problem in a
Central Potential. The General
Effective Potential for the Two-Body
Problem. Kepler Problem.
|
02/18
02/20
02/22
|
Reading Week No Classes
|
| 02/25 |
Two-Body 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
|
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