Send comments or questions to: ldurand@hep.wisc.edu           

 

Instructor:

L. Durand, 4209 Chamberlin. Email address: ldurand@theory2.physics.wisc.edu Web site: http://theory2.physics.wisc.edu/~ldurand/ Telephone: 262--3996.

Meets:

11:00 MWF, 3401 Sterling Hall

Office hours:

I'm around most of the time. Feel free to stop in with questions or comments (except the hour before class!), or check after class, by email, etc., for a definite time to come by.

Objectives of the course:

Physics 711 is a course in theoretical mechanics. It is intended as an introduction to the formal structure and applications of classical mechanics. The main emphasis in the course will be on the aspects of mechanics -- Lagrangian and Hamiltonian mechanics, symmetries, rotations, relativity, oscillations -- which are most important as background for quantum physics and other areas of theoretical physics and mathematics. Many of the applications we will consider are to material that "every physicist is expected to know" -- here's your chance to learn it!

Course content:

Topics to be covered include the Lagrangian form of mechanics, variational principles, symmetries and conservation laws, small-oscillation problems, rotations and the motion of rigid bodies, relativistic kinematics and dynamics, Hamilton's equations and canonical transformations, the symplectic structure of Hamiltonian mechanics, Poisson brackets, infinitesimal canonical transformations and conservation laws, and Hamilton-Jacobi theory.

See the syllabus for more details.

Further topics in mechanics, including the dynamics of classical fields, more on the structure of Hamiltonian mechanics and Hamilton-Jacobi theory, perturbation methods, and mappings, are covered in the Spring semester in Physics 722 -- see the Spring, 1998, 722 course description and syllabus. The remainder of 722 deals with relativistic and particle electrodynamics.

Text:

H. Goldstein, Classical Mechanics, plus selected readings in books on reserve in the Physics Library (see the comments below).

Homework:

The course is problem-based, and there will be problem sets most weeks. The problems are often challenging, but are directed to real physical applications, so are correspondingly interesting. The web version of the assignments includes hints and extra comments on the physics involved!

You are strongly encouraged to discuss the problem assignments with other students in the class, and to work together on their solution. I am happy to discuss the problems with you and give hints, but you may learn more from your fellow students! Most physics is done in collaborations, and this approach is intended to give you a chance to develop the skills in working on real problems in a collaborative setting that are expected by most potential employers of physicists.

I will put problem solutions on reserve in the Physics Library after the due date. Be sure to look at the the solutions! I often add extra remarks on the physics involved.

Exams and grades:

There will be three hour exams, probably on Wednesday, October 14 and Wednesday, November 18 during the regular class hour, and at 2:45pm Tuesday, December 22 during the final exam period. Each will count 25% of the final grade. The homework counts as the final 25% of the grade.

My grading scale for this course is normally 87-100 for A, 70-86 B, 60-69 C, with AB used in the area approaching the B to A transition. I don't raise the cutoffs, but may dip below the levels stated if an exam turns out to be too hard, if a person started poorly but demonstrated real improvement during the semester, or in other exceptional circumstances.

Reserve books:

The following books will on reserve in the Physics Library, 4220 Chamberlin. There are many other books that you might find useful. Browse through the stacks in the general classification QA 805-845.

Intermediate mechanics

• K. Symon, Mechanics -- very thorough, excellent problems.

• V. Barger and M. Olsson, Classical Mechanics -- takes a Lagrangian approach to mechanics.

• A. Sommerfeld, Mechanics -- delightful, good on history.

Graduate mechanics

• H. Goldstein, Classical Mechanics -- the text.

• L.D. Landau and E.M. Lifschitz, Mechanics -- very physical, derivations sketchy.

More advanced graduate level

• V.I. Arnol'd, Mathematical Methods of Classical Mechanics -- among the best books, by one of the principal contributors to modern developments in mechanics -- "reads PG, but should be classified X" (L. Leavitt).

• E.T. Whittaker, Analytical Dynamics -- classic treatise, well worth studying; very detailed derivations, only one or two figures in the book.

• L.A. Pars, A Treatise on Analytical Dynamics -- excellent and very complete; high level, but a good reference with many recent examples.