Physics 821 (Autumn, 2009)

Introduction and General Format

Physics 821 is a one quarter graduate course on classical mechanics. The text will be "Classical Mechanics," 3rd edition, by Herbert Goldstein, Charles P. Poole, and John L. Safko (Addison-Wesley, San Francisco, 2002; ISBN 0-201-65702-3; list price $142.20, currently available on amazon.com for$119.21 or less).

The instructor is David Stroud. The grader is Eugene Hong (room PRB3018, tel. 614-214-2718, email ripple80@gmail.com).

We will meet in Smith Lab, Room 1048, on Tuesdays and Thursdays from 9:30 to 10:18 and 10:30 to 11:18.

Grades will be based on one midterm, a final, and homework. The relative weightings of these will be approximately 25, 40, and 35% respectively.

The midterm is scheduled for Tuesday, November 3, 2009. The final will probably be given on the date listed in the registrar's schedule of final exams, i. e. Thursday, December 10 from 9:30 to 11:18.

Besides the principal textbook, I may occasionally take some material from various other books. Some other well-known books on the subject of advanced mechanics are the following:

Mechanics,'' 3rd edition, by L. D. Landau and E. M. Lifshitz. A classic text, which covers most of the material that I will teach, though quite tersely.

Theoretical Mechanics of Particles and Continua,'' by Alexander L. Fetter and John Dirk Walecka. The first six chapter correspond roughly to the material of Physics 821.

Classical Dynamics: A Contemporary Approach'' by Jorge V. Jose and Eugene J. Saletan. Includes treatments of nonlinear dynamics and chaos, continuum mechanics, and various advanced mathematical techniques. Last year's text.

Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering,'' by Steven H. Strogatz. Suitable for a special topics course on nonlinear dynamics, written by someone who has made important contributions to this field.

Classical Mechanics,'' by John R. Taylor. Written as an advanced undergraduate text, but said to be extremely clear and useful to graduate students also.

Syllabus

I expect to cover much (but not all) of the material in Chapters 1-6 of the text, plus part of Chapter 8 (Hamilton's equations). If I have time (not very likely), I might try to do something from chapters 11 or 13. I will probably skip Chapter 7 (special relativity) since this is also covered in classical electrodynamics.

Note: a good online math reference is http://mathworld.wolfram.com, which has lots of analysis, plus a great deal of information about special functions. Two good books are "Tables of Integrals, Series, and Products," 6th ed., by Gradshteyn, Ryzhik, Jeffrey, and Zwillinger (Academic, San Diego, 2000), and "Mathematical Methods for Physicists," by Arfken, Weber, and Weber (Academic, San Diego, 2001).

Problem Sets

I plan to have weekly problem sets, mostly due on Thursdays. The tentative due dates are October 1, 8, 15, 22, 29, November 5, 12, 19, and December 1 (Tuesday). If possible, turn in the problem sets into the mailbox of the grader, Eugene Hong, in PRB. Alternately, you may turn them into my mailbox, turn them in during class, hand them to me in my office, or or slip them under my office door (2048PRB) if I am not there.

In calculating the homework grade, I will sum up the homework scores, and covert the sum to a percent.

In general, I do not object if you discuss the problems with one another while working on them. However, you must write up your solutions independently.

I will not have any required reading. However, I will try to suggest sections of the text to be read before or after my lectures.

oProblem Set 1.

There is a minor misprint in Problem Set 1: Problem 3 is an exercise,'' not a derivation''.

oSolutions to PS1.

oCorrection to solution of problem 4 of set 1.

oProblem Set 2.

oSolutions to PS2.

oProblem Set 3.

oSolutions to PS3.

oProblem Set 4.

oSolutions to PS4.

oProblem Set 5.

oSolutions to Problem Set 5, problems 1, 3, and 4.

oSolutions to Problem Set 5, problem 2, and correction to solution to problem 1. Note: at the end of the solution to problem 2, it should read dx = d\theta/\pi, not the other way around.

oProblem Set 6.

oSolutions to PS 6.

oProblem Set 7.

oSolutions to PS 7.

oProblem Set 8.

oSolutions to PS8.

My office is Room 2048 of the Physics Research Building. My office telephone no. is 292-8140 and my email address is stroud@mps.ohio-state.edu. I will have office hours Tu 1-2 PM and Th from 11:30 to 12:30. You can also see me by appointment, or you can simply drop by, and I am generally happy to talk to you if I do not have another visitor. Please consult the grader, Eugene Hong, if you have any questions about the homework grading.

Lecture Notes

I expect to post my (hand-written) lecture notes as I complete them. They are posted as a study aid but they are not guaranteed to be error-free. (In fact, they are almost guaranteed to be non-error-free.)

oFirst set of lecture notes (lecture of Sept. 24: mostly momentum, angular momentum, and energy conservation).

oA simple way to prove conservation of energy for an N-particle system in which the forces are expressible as gradients of a potential.

oSecond set of lecture notes (lecture of Sept. 29: derivation of Lagrange's equations from Principle of Least Action; inertial frames; form of Lagrangian for a free particle and particles interacting via a potential).

oThird set of lecture notes (lecture of October 1: calculus of variations; several examples; more simple examples of Lagrangian mechanics; Lagrangian corresponding to Lorentz force).

oFourth set of lecture notes (lectures of October 6 and 8: Lagrange multipliers; forces of constraint; examples; start of central forces).

oFifth set of lecture notes (lectures of October 13 and 15: central forces, Kepler problem, virial theorem

oSixth set of lecture notes (mostly scattering from a central potential).

oSeventh set of lecture notes (kinematics of rigid body motion: rotations and their description by orthogonal matrices; review of some aspects of linear algebra).

oEighth set of lecture notes (more kinematics of rigid bodies: Euler angles, Euler's theorem).

oNinth set of lecture notes (infinitesimal rotations; Coriolis effect; equations of motion in a rotating frame of reference; start of rigid body dynamics; moment of inertia tensor).

oTenth set of lecture notes (more on rigid body dynamics; symmetric top with and without a gravitational field).

oEleventh set of lecture notes (small oscillations).

oTwelfth set of lecture notes (Hamiltonian formulation of mechanics; Poisson brackets; driven small oscillations).

Random Information

oIsaac Newton

oJoseph Louis Lagrange

oLeonhard Euler

oPierre Louis Maupertuis

oWilliam Rowan Hamilton

o Gaspard-Gustave de Coriolis