Updates:

• 12/14  Final exam statistics (Ave/Out of [SD]):
  Question 1: 13.2/30 [6.5]; (Max 22, Min 0)
  Question 2: 30.1/40 [7.3]; (Max 38, Min 11)
  Question 3: 20.9/30 [6.9]; (Max 29, Min 2)
       TOTAL: 64.2/100 [16.7]; (Max 85, Min 13)
  

  As you can see from the results, the first question was found to be the most difficult. Many students tried to solve using the Euler equations, which turns out to be more complicated than simply using L-dot=torque. For completeness, and in case anyone is interested, a solution using the Euler equations is posted here. I also include a note on the correspondence between the angles used in the problem and the canonical Euler angles.
  

  My solutions for the last problem had one error---the shape of the trajectories depend on the amplitude. For a purely quartic potential then are squashed horizontally at large amplitudes but then switch over to being squashed vertically one the amplitude drops below about unity.

  I will put final exams into mailboxes tomorrow (for those with mailboxes). For others, I will have them in my office. Have a good break!

• 12/4   Thanks to Isaac for finding a reference on Synchronization of metronomes: by James Pantaleone, American Journal of Physics, October 2002, Vol. 70, issue 10, pp. 992-1000. See AJP for the journal home page, from which you can go to the journal. If you do so from a physics machine you can download the paper. Turns out that
• 12/1   Mechanics melody (courtesy of Christian B.) posted in "useful links" below.
• 11/7   Midterm statistics (Ave/Out of [SD]):
  Question 1: 13.9/22 [3.8]; (Max 19, Min 7)
  Question 2: 5.8/8 [2.3];    (Max 8, Min 0)
  Question 3: 16.6/20 [4.9]; (Max 45, Min 19)
       TOTAL: 36.3/50 [7.3]; (Max 45, Min 19)
  

Office hours and contact information

• Prof. Steve Sharpe   srsharpe@uw.edu   B406 PAB  685-2395
• Office hours: Mon 1-2, Tues 1:15-2:15
• TA: Andrew Lytle   alytle@u.washington.edu   B422 PAB  543-9642
• Office hours: Tues 5-6pm

Texts

• "Theoretical Mechanics of Particles and Continua," by A.L. Fetter and J.D. Walecka (Dover reprint series)

• "Chaotic Dynamics: An Introduction," by G.L. Baker and J.P. Gollub (Cambridge University Press; 2nd ed. 1996)

Course Structure and Syllabus

• This course is a mix of about two thirds standard classical mechanics (covering material that can appear on the corresponding section of the qualifying exam), and one third chaotic systems. Last year's daily coverage serves as a good, though approximate model for this year's course. We have one more lecture this year, which I may use to go more deeply into Hamiltonian Dynamics.

  A less detailed outline is as follows (FW = Fetter and Walecka, BG = Baker and Gollub):

  • Introduction and review of Newtoninan Mechanics (FW Chs. 1 & 2)
    • Central forces, orbits, scattering
    • Inertial and non-inertial reference frames
  • Lagrangian Dynamics (FW Ch. 3)
  • Small Oscillations and Normal Modes (FW Ch. 4)
  • Rigid Bodies (FW Ch. 5)
  • Hamiltonian Dynamics (FW Ch. 6)
  • Introduction to chaos---phase space flows, attractors (BG Ch. 1)
  • Forced, damped pendulum as the examplar of chaotic behavior---Poincare maps, bifurcation diagrams, period doubling route to chaos (BG Chs. 3 and 4)
  • General characterizations of chaotic systems: self-similarity and fractal dimensions, Lyapunov exponents, intermittency. (BG Chs. 5 and 6)
• Reading ahead and archived handouts.
  • I will note in the daily coverage topics that I expect you to read about before the next lecture. This link also archives any handouts.
• Holidays.
  • There will be no class on the day after Thanksgiving (Friday, November 28th).
• Homework.
  • There will be weekly homework sets, usually due on Wednesdays in class, probably ten sets in all. These will be made available on the homework and solutions link.
  • You are encouraged to discuss the assignments with classmates, but the solutions you turn in must be your own work.
  • Many of the problems during the section of the class on chaotic dynamics will require the use of a program such as Mathematica or Maple. Gaining experience with and mastery of such programs will be useful for other classes and for your future research.
  • Working on assignments in a timely fashion is an important part of the learning process. Late work will be accepted at the class meeting subsequent to the due date, but with a 50% penalty. After that, assignments will not be accepted, unless as prearranged due to exceptional circumstances.
  • Solutions will be posted on the homework and solutions link, typically after the lecture following the due date. Graded homework sets will be returned about a week after their due date.
• Exams. There will be two exams in this class:
  • The midterm will be on Wednesday November 5th, in class. The previous lecture will be devoted to a review.
  • The final exam will be on Tues, December 9th, 10:30-12:20pm in A114 (our regular lecture hall).
  • Solutions to exams will be posted on the homework and solutions link, along with grade statistics.