Department of Physics, College Park, MD 20742
Physics 601----Classical Mechanics----Fall 2009
Instructor: Prof. Thomas Cohen
(I prefer to be addressed as Tom)
Office: 2104 (Physics Building)
Phone: 5-6117 (Office); 301-654-7702 (Home---call before 10:00 p.m.)
Office hours are immediately following class. I am also generally available in my office and happy to see students; just drop by--or, better yet, give me a call and then drop by.
Classical mechanics is an exceptionally beautiful and powerful subject. This class will focus on both its formal aspects and on important classes of applications. The first section of the course focuses on formal approaches, Lagrangians, Hamiltonians, canonical transformations, Hamilton-Jacobi approach and the like. The second section part of the course deals with applications such as scattering, small vibrations, central force problems, rigid-body motion and relativistic dynamics. A final section of the course will deal with some aspects of non-linear systems. Depending on the amount of time available this will deal with classical perturbation theory and other approximation methods in classical mechanics and perhaps some aspects chaotic dynamics.
The course assumes that you have had a strong undergraduate background in classical mechanics. If this is not the case please review a standard undergraduate classical mechanics book such as Classical Mechanics, by John R. Taylor or Classical Dynamics of Particles and Systems by Thornton and Marion
The offical text for the course is Classical Dynamics: a Contemporary Approach by Jose and Saletan (ISBN 0-521-63636-1). The book is quite sophisticated; while it covers material in a standard graduate course, it also has extensive discussions on topics well beyond this. Thus the book should prove to be a useful reference work once the class is over. Advanced topics include very elegant treatments of classical systems in terms of differential geometry using tangent bundles and the like. While we will not make extensive use The course will not generally closely follow Jose and Saletan. However, the book will provide an essential supplement to the lecture material.
Problem sets will be assigned regularly. Problem sets may require the use of numerical analysis that can be done in Mathematica or some other computer program. I strongly encourage students to consult each other on problem sets. Ideally you should attempt all of the problems by yourselves and if you get stuck you should then consult your peers. Homework will count approximately 20% of the final grade. Not all problems will be graded---a representative sample will be. A set of solutions to the homework problems prepared by the TA will be posted on the course web cite for additional feedback. These solution sets may in part consistent of corrects solutions submitted by students in the course. If you object to your homework being used as a solution set, please indicate this on your homework (or simply do a lousy job on your homework).
There will be a midterm
exam and a final exam in this course. The exams will count for approximately
80% of the total course grade. The exams are currently planned as take-home. Take-home exams have two
virtues: they reduce the time pressure on students and allow them to perform at
their best and they allow for questions that are less trivial than can be done
during a class period. They do have a potential drawback, however. They are
impossible to police efficiently against cheating. Thus, we must rely on your
integrity. I will ask you to pledge to do the exams alone and to stick to this
pledge. I should note that the whole enterprise of science depends on the
integrity of the researchers--- when I read a scientific paper I must assume
that the researchers didn't cook the books or I won't get anywhere.
Tentative Course Outline
· Formal aspects
o Lagrangian Approach
§ The variational principle and the equations of motion
§ Symmetries and conservation laws
§ Continuum dynamics, field theory and wave equations
o Hamiltonian Approach
§ Hamilton’s equations
§ Possion brackets
§ Canonical tranformations
§ Liouville’s theorem
§ Hamilton-Jacbi Equation
§ The adiabatic theorem
o Systems with one degree of freedom
o Magnetic systems
o Central force problems
§ The Kepler problem
o Classical scattering theory
o Coupled linear systems; small oscillations
o Rigid-body motion
§ Euler angles
§ The Euler equations
o Relativistic Dynamics
· Nonlinear Dynamics
o Classical perturbation theory
§ Resumed perturation theory; applications to the nonlinear oscillator
o Topics in chaotic dynamics.