**University
of Maryland**

**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.)

**E-mail:** cohen@physics.umd.edu

**email: **ysubasi@gmail.com**
**

**Office
Hours**

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.

**Course
Philosophy**

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

**Books**

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.

**Homework**

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).

**Exams**

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.

** **** **

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****Tentative Course Outline**

· Formal aspects

o Lagrangian Approach

§ The variational principle and the equations of motion

§ Constraints

§ 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

· Applications

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.