**University
of Maryland**

**Department of
Physics, College Park, MD 20742 **** **

**Physics
601----Classical Mechanics----Fall 2010**

**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

**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. 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 and dynamical systems.

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 official text for the
course is *Classical
Dynamics* by Goldstein, Poole and Safko* *(ISBN
0-201-65702-2)*.
*The book is the canonical graduate classical mechanics book and covers the
topics in a straightforward way.
The course lectures will not follow the book closely, however the book
will give useful alternative explanations for things covered in lecture. Those who wish to approach things from
a more sophisticated mathematical framework including

differential geometry using tangent bundles and
the like may find it interesting to look at Jose and Saletan,
*Classical
Dynamic: A Contemporary Approach*.

**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-Jacobi Equation and Action-Angle Variables

§ Classical Perturbation Theory

§ Adiabatic Invariance

· Applications

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 Resumed perturation
theory; applications to the nonlinear oscillator

o Topics in chaotic dynamics.