Course Schedule and Syllabus

Tentative Schedule

Please check back regularly for updates with each week’s topics (the general outline of the course can be found in the syllabus below.) The reading assignments refer to Goldstein’s (G) and Taylor’s (T) books, respectively.

Week Dates Topics Reading Homework Due
1 We 8/28 -
Fr 8/30 		Logistics, Themes, Newtonian Mechanics Recap G: 1.1-1.2
T:
1-4 This is indeed chapter 1-4. Taylor's book contains a comprehensive discussion of Newtonian Mechanics.
 HW01 9/6
Mon 9/2 Labor Day (no classes)
2 We 9/4 -
Fr 9/6 		Constraints, D'Alembert's Principle G: 1.3-1.4
T: 7.1-7.4 		HW02 9/13
3 Mo 9/9 -
Fr 9/13 		Variational Calculus, Principle of Least Action
Lagrange Equations of the First and Second Kind 		G: 2.1-2.5
T: 6, 7.4-7.5, 7.10 		HW03 9/20
4 Mo 9/16 -
Fr 9/20 		Noether's Theorem, Symmetries G: 2.6-2.7
T: 7.6-7.8 		HW04 9/27
5 Mo 9/23 -
Fr 9/27 		Velocity-Dependent Potentials, Dissipation G: 1.5-1.6
T: 7.9, 5 		HW05 10/7
6 Mo 9/30 -
Fr 10/4 		Oscillators, Damping, Driving Forces G: 6.1-6.4
T: 5 		HW06 10/11
Fr 10/04 Midterm 1, 11:30am-12:20pm, BPS1420
7 Mo 10/7 -
Fr 10/11 		Coupled Oscillators, Normal Coordinates G: 6.1-6.4
T: 5 		HW07 10/18
8 Mo 10/14 -
Fr 10/18 		Central Forces, Orbits G: 3
T: 8 		HW08 10/25
9 Mo 10/21 -
Fr 10/25 		Orbits, Scattering G: 3.7, 3.9-3.11
T: 8, 14 		HW09 11/1
10 Mo 10/28 -
Fr 11/1 		Three-Body Problem, Lagrange Points, Non-Inertial Frames G:3.12, 4
T:8, 9 		none
(midterm prep)
11 Mo 11/4 -
Fr 11/8 		Rotations, Euler Angles G:4
T:9, 10 		HW11 11/15
Fr 11/8 Midterm 2, 11:30am-12:20pm, BPS1420
12 Mo 11/11 -
Fr 11/15 		Rigid Body Kinematics, Inertial Tensor G: 4, 5
T: 10 		HW12 11/22
13 Mo 11/18 -
Fr 11/22 		Rigid Body Dynamics, Steiner and Intermediate Axis Theorems, Hamiltonian Mechanics G: 4, 5, 8, 9
T: 10, 13 		HW13 12/2
14 Mo 11/25 -
We 11/27 		Phase Space, Liouville's Theorem, Poisson Brackets and Canonical Transformations G: 8, 9
T: 13 		HW14 12/6
Fr 11/29 Thanksgiving weekend (no classes)
15 Mo 12/2 -
Fr 12/6 		Poisson Brackets and Canonical Transformations (cont'd) G: 8, 9
T: 13
We 12/11 Final Exam, 7:45-9:45am, room tbd

Syllabus

The course will cover the following topics:

  1. Lagrangian Mechanics
    • constrained motion
    • D’Alembert’s principle
    • Principle of Least Action
    • Euler-Lagrange equations of the first and second kind
    • Noether’s theorem and symmetries
    • applications, e.g., coupled oscillators
  2. The Kepler Problem
    • orbits and stability, Bertrand’s theorem
    • conserved quantities
    • perihelion precession
    • scattering
    • Lagrange points
  3. The Rigid Body
    • rotating coordinate systems
    • Euler angles
    • inertia tensors and principal axes
    • Euler equations
    • free rigid body
    • wobbling motion
  4. Hamiltonian Mechanics
    • Hamiltonian equations of motion
    • phase space
    • canonical transformations
    • Poisson brackets

Depending on our progress, we will discuss some of the following topics:

  • Nonlinear Dynamics
    • anharmonic oscillators
    • perturbative treatment; Lindstedt-PoincarĂ© method
    • numerical solution
    • examples of chaotic behavior
  • Classical Field Theory
    • elements of special relativity: Lorentz transformations, Lorentz tensors
    • Lagrangians in field theory
    • equations of motion
    • spontaneous symmetry breaking
  • Fluid Dynamics