Bryn Mawr College
Physics 308: Advanced Classical Mechanics
Fall 2011
Tue, Thr 11:15 - 12:45
Park 337
Recitation TBD
Office Hours TBD
James Battat
Park 345, x7846
jbattat@brynmawr.edu
http://www.brynmawr.edu/physics/courses/308
Course Description
This course is, on one hand, an extension of your first course on mechanics, but on the other a
springboard into modern physics. Beginning with a recap of Newton’s laws, and conservation laws,
we will branch out to a deep study of oscillatory behaviour and explore the power of Fourier analysis.
Then the real fun begins. We will develop the Lagrangian and Hamiltonian frameworks (good-bye
force diagrams), and see that they not only allow us to solve for the motion of bodies in complicated
systems, but also that they underpin much of modern theoretical physics: quantum mechanics and
particle physics and quantum field theory and gravitational physics and the list goes on. In addition
to preparing you for further study in these areas, this course will reveal a deeper connection between
mathematics and physics, and between diverse subfields of physics.
Required Textbook
Classical Mechanics, John R. Taylor, University Science Books (2005), ISBN 1-891389-22-X
Course Assignments
Problem sets: There will be regular homework assignments. Some problems will involve Mathematica
to find analytical and numerical solutions to mechanics problems. Prior experience with programming
is certainly not a pre-requisite. Each problem set will contain at least one problem that is designated
as “independent.” You must work through this problem on your own, without discussing it with
others. You may, however, use library resources. For the other problems, I encourage you to work
together, though what you hand in must be representative of your own work, not a reproduction of
the work of others. I find that students both learn from and contribute more to group work when
they have each individually grappled with the problems first. In all cases, it should go without saying
that searching for solutions to homework problems online (or elsewhere) runs counter to the spirit of
the educational process and is not permitted.
Exams: There will be two mid-term exams and a final exam. All will be closed-book, but you may
populate one page of paper with whatever information you like.
Independent project: Classical mechanics is a broad discipline, and in this course we will certainly
not cover it all. In recognition of diverse student interests, you will extend the reach of this course
through an independent study project that culminates in a paper (due at the end of the semester) and
a brief presentation to the class. This paper will be five to ten pages long and could focus on classical
mechanics or its applications to (e.g.) physical, chemical, biological phenomena or to engineering or
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social sciences. The paper must contain mathematical detail at the level appropriate to the course.
We will discuss topics as the semester progresses, and you will submit a draft for review as well.
Grading
Weights:
• Homework: x% (see below)
• Midterms (2): 20% each
• Independent Project: 15% (draft & final paper)
• Final Exam: (45-x)%, where x is a real number, chosen by you, in the range [10,30]. You must
choose x by the last day of class. By default, x = 20.
Homework: I will read all of your solutions, but will only grade the “individual” problems and a subset
of the others (sometimes, that subset will be the entire set). The “individual” problems will carry
more weight. For full clarity and credit, it is necessary to write down in detail the path that you took
from question to solution. In most instances, this requires explanatory prose in addition to equations.
Extensions: Late homework will not be accepted, unless pre-arrangements have been made (please
only ask when you have a legitimate need). The caveat is that each student gets one “free extension”
for a problem set without penalty. To use the extension, simply turn in a piece of paper with your
name, the assignment number, and the statement that you are taking your “free extension.” You then
have one week to turn in your problem set to receive full credit.
Accommodations
I have a moderate hearing loss and wear hearing aids in both ears. Generally, in settings like ours,
I have little trouble hearing. But please be aware that I may ask you to repeat your questions or
your answers to mine. Interestingly, the topics of sound waves and human auditory response lend
themselves nicely to the study of Fourier series, a core component of this course.
Anyone who requires accommodations in this course because of the impact of a learning, physical, or
psychological disability are encouraged to discuss their needs with me privately early in the semester
(I can’t help if I don’t know about it). In addition, students must contact Stephanie Bell, Coordinator
of Access Services (610-526-7351 or sbell@brynmawr.edu), as soon as possible, to verify their eligibility
for reasonable academic accommodations. Early contact will help to avoid unnecessary inconvenience
and delays.
Supplementary Materials on Reserve in Collier Library
• Mechanics texts
Feynman, Leighton & Sands, The Feynman Lectures on Physics, Volume 1
Marion & Thornton, Classical Dynamics of Systems and Particles
Fowles & Cassidy, Analytical Mechanics
Landau & Lifshitz, Mechanics
Goldstein, Poole & Safko, Classical Mechanics
• Mathematical Methods
Boas, Mathematical Methods in the Physical Sciences
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Course Schedule
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Dates
Aug. 30
Sep.
1
6
8
13
15
20
22
27
29
Oct.
4
6
11
13
18
20
25
27
Nov.
1
3
8
10
15
17
22
24
29
Dec.
1
6
8
Topic
Taylor
Review & Newton’s Laws
Chap. 1
Linear & angular momentum
Chap. 3
Energy & conservation laws
Chap. 4
Oscillations: damped, driven, resonance
Chap. 5
Fourier series
Chap. 5
Calculus of variations
Chap. 6
Notes
Survey due Th.
HW 1 due Th.
HW 2 due Th.
HW 3 due Th.
Paper topic due Tue.
HW 4 due Tue.
Exam 1 due Fri.
FALL BREAK
Lagrangian mechanics
Chap. 7
Lagrangian & Hamiltonian mechanics
Chap. 7 & 13
Central forces & planetary motion
Chap. 8
Accelerated reference frames
Chap. 9
Rotation of rigid bodies
Chap. 10
Collisions and scattering
Chap. 14
THANKSGIVING
Coupled oscillations & normal modes
Chap. 11
Normal modes
Wrap-up
Chap. 11
3
HW 5 due Tue.
HW 6 due Thr.
Paper draft due Tue.
HW 7 due Thr.
Exam 2 due Tues.
HW 8 due Tue.
Paper due Thr.