Physics 321b: Advanced Classical Mechanics

Spring 2014

Course meets: Tuesdays and Fridays from 2:30 - 4 pm, in Elliott 162
Fearless leader: Justin Albert
Office: Elliott 213
Office Phone: (250) 721-7742
Cell Phone: (250) 661-7066
E-mail: jalbert AT uvic DOT ca
Labs led by Alex Wong

Office hours: Come by anytime! I will stay in my office for an hour after each class, but please send e-mail or call if you want to be absolutely sure I will be in my office/available at any given time. If I'm in my office but busy I'll let you know a time to come back. Feel free to always try my office though, or phone, or e-mail. Cell phone is (250) 661-7066, feel free to call! My lab space is in Elliott 022, and you can sometimes find me there too.

Course homepage: https://particle.phys.uvic.ca/~jalbert/321b/index.html

Text (required): Alexander L. Fetter and John Dirk Walecka, Theoretical Mechanics of Particles and Continua, McGraw-Hill, 1980.
You can get (a new softcover or used hardcover of) this textbook for $30 or less online -- so absolutely no need to pay $120 or so for a brand-new hardcover, unless you want to. The only difference between the 1st edition (from McGraw-Hill) and the 2nd edition (from Dover) is in the preface(!), so there's absolutely no need to get a recent version -- classical mechanics certainly hasn't changed dramatically in the last 30 years, so there's no good reason to hand an additional $90 over to publishing companies. Please try to read the sections assigned on the syllabus before the indicated lecture!

Some other sources that I consult:
Landau + Lifshitz, Mechanics (Course of Theoretical Physics vol. 1), Pergamon Press, 1969. (free online pdf!)
Marion, Classical Dynamics of Particles and Systems, Academic Press, 1970.

Prerequisites: Physics 321a

Midterm Date: Friday, Feb. 7 (in class) -- here is the midterm and its solutions -- here are some practice problems (.pdf) and their solutions (.pdf). We'll have a review session (optional but useful) at 5:30 pm on Wednesday, Feb. 5 in Ell 162 (the usual classroom)
Final date: Monday, Apr. 14 at 9 am in Cornett A121 -- we'll have a review session at 2 pm on Wed., Apr. 9 in Ell 162 (the regular classroom) -- here are some practice problems and their solutions.

Schedule
This syllabus is incomplete and tentative, and will be superseded by later versions as the course evolves.

Lecture	Topic	Sections	Homework
1	Generalized Coordinates, and the Principle of Least Action lect notes	1 - 5	----
2	Galilean Relativity, and the Lagrangian	6 - 12	(due Fri., Jan. 17) Fetter+Walecka problems 3.1 and 3.2 (sketch), and Landau+Lifshitz problems 1.1, 1.2, and 1.4 solns
3	The Lagrangian for a System of Particles	13 - 18	----
4	Energy and Momentum	19	(due Fri., Jan. 24) Fetter+Walecka problems 2.2 (in this problem, please additionally rederive the equations of motion (11.8) and (11.5a) using Lagrange's equations), and 3.5; and the two Landau+Lifshitz problems respectively on p. 16 and 18 of L+L solns
5	Centre of Mass and Angular Momentum	20	----
6	Mechanical Similarity and Motion in One Dimension	21	(due Tue., Feb. 4) Fetter+Walecka problem 3.8; and Landau+Lifshitz p. 21 problem 3, p. 24 problems 1 and 2, and p. 27 problem 2 solns
7	Oscillations, Potential Energy, and Reduced Mass	22	----
8	Motion in a Central Field, and Kepler's Problem		(due Tue., Feb. 25) Fetter+Walecka problems 1) 4.6 and 2) 4.7, and 3) Investigate the motion of a particle which is repelled by a force centre according to F(r) = kr, for some constant k, and show that the "orbit" can only be hyperbolic.
9	Elastic and Inelastic Collisions, and Disintigration		----
10	Scattering and Rutherford's Formula		(due Tue., Mar. 4) Fetter+Walecka problem 1.16, and Landau+Lifshitz p. 50 problem 1
11	Free and Forced Oscillations in One Dimension	23	----
12	Oscillations in More Than One Dimension, Molecules	24	(due Fri., Mar. 14) Fetter+Walecka problem 4.12, and Landau+Lifshitz p. 64 problems 1 and 2
13	Damped Oscillations With and Without Forcing	25	----
14	Parametric and Anharmonic Oscillations		(due Tue., Mar. 25) Fetter+Walecka problem 4.9, and Landau+Lifshitz p. 72-73 problems 1 and 2. (Please try the L+L problems before the F+W one -- I think you'll probably find that easier. Also, in each of these problems, of course, please discount quantum mechanical effects, even though oscillations of real molecules are quantum mechanical.)
15	Resonance in Nonlinear Oscillations, and Motion in a Rapidly Oscillating Field		----
16	Angular Velocity and the Inertia Tensor	26	(due Fri., Apr. 4) Landau+Lifshitz p. 102 problem 3 (do this first), and then Fetter+Walecka problem 5.1 parts (a) and (c) (not part (b)).
17	Angular Momentum and the Equations of Motion
18	The Euler Angles and Euler Equations	27 - 29
19	Asymmetric Tops, and Rigid Bodies in Contact	30, 31
20	Motion in a Non-Inertial Frame of Reference
21	Hamilton's Equations, and the Routhian	32, 33
22	Poisson Brackets, and the Action	36, 37
23	Maupertuis' Principle, and Canonical Transformations	34
24	Liouville's Theorem, and the Hamilton-Jacobi Equation	35
25	Separation of Variables, and Adiabatic Invariants	Appendix C
26	Beyond Classicality

Grade will be based 30% on the weekly problem sets above, 15% on a 1-hour midterm exam, 20% on your laboratory work, and 35% on the final exam. Your lowest problem set score will be dropped.
Please note I keep my average grades equal to those of other 300 level courses in phys + astro at UVic, i.e. the average grade in the course will likely be a B or so, similar to the other 300 level courses from other faculty in the department. If the class is especially good, I will move this upward -- and down a bit if you're horrible beasts! -- but the class average will likely be approximately a B. I don't use formulas such as 80-100=A, 70-80=B, etc. Some of my assignments or tests can be hard (but good!), in which case the average may be a 50 or even below. DON'T WORRY if that's the case and you get a 50. That's the same as getting a 90 on an easy test in which the class average is a 90. You might pay more attention (if you're super-concerned about grades) to the average score in the class and the standard deviation (which I will mention after each assignment), and how yours compares with the average.

Problem sets: Problem sets are due at the beginning of class on Friday (first one due on Fri., Jan. 17th). Answers will be posted the following Friday.

You are allowed one late homework without penalty, up to a week late (along with the one lowest problem set score that is dropped). All other late homeworks count 50% if completed before the answer key is handed out the following week. Afterwards, it counts 10% (there is still a little bit of value in copying over the answers to better understand them). No exceptions (other than death in the immediate family, signed doctor's note). Note that the lowest homework score is dropped, and another homework can be a week late, so that covers cold/flu issues.

Collaboration on the homework is at your discretion. Each person is responsible for doing his/her share of the work, writing up her/his own solutions and for listing his/her collaborators on each set.

Exams are closed book, closed notebook. You will be allowed to bring an 8.5" x 11" formula sheet of your own making (double-sided) to each exam.

Calculator: The only acceptable calculator for student use on exams (as per the department policy) is the Sharp EL-510RB. It is available at the UVic Bookstore for $8.95.

The midterm exam will be held in class. No makeups will be given (other than the above death in the immediate family, signed doctor's note).

Please let me know anytime if you have any questions!!!