Phys 601: Theoretical Dynamics
Fall 2004, Section 0101
MWF 9:00-9:50, Room Symons 0200
Instructor:
Room 2107, Phone 301-405-7128 E-mail: stevewal@physics.umd.edu, Office hours: Tu,Th 1:30-2:30. Feel free to drop in. |
Teaching Assistant:
Room 3101 , Phone 301-405-6194 mystyle@mail.umd.edu Office hours Monday 4-5PM, Tuesday 2-3 PM : |
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Solution to Final Exam. posted at link below. Have a good holiday. |
Links to other pages for course:
Textbook
H. Goldstein, C. P. Poole and J. L. Safko
Classical Mechanics, Third Edition,
(Addison-Wesley, Reading Massachusetts), ISBN: 0-201-65702-3. Copyright 2002.
This book had numerous errors in early printings. See the following web site. It tells how to find out what printing you have and gives lists of corrections that have been made in recent printings. Corrections to early printings |
E-mail: I encourage students to make use of e-mail for quick correspondence with me regarding lecture material, homework problems, or whatever. I will also use e-mail to communicate with the class at large.
Homework: Assigned weekly and due the following week. Late homework accepted at 75% full value up to 5:00 PM two days following due date. If you know it will be impossible to turn in an assignment on time you must discuss this with me in advance of the due date. Sources (e.g. textbooks or classmates) should be cited when used heavily in a homework solution. Please make sure you include your name and the homework and course numbers and staple the pages together.
Exam Schedule ..........Midterm Examination I: Wednesday, October 20 ..........Midterm Examination II: Monday, November 29 ..........Final Examination Thursday, Dec. 16, 2004 8:00am-10:00am, Symons 0200 |
Grading: Based on homework (30%), mid-term exams (40%), and
final (30%),
Final Exam score will be used to decide borderline cases.
A rough guide is that 50% - 60% of the overall points plus a passing
score on the final exam are required to earn a grade of B- or better.
Reserve books:
Chapters 1 and 2 of Goldstein cover the basics of lagrangian mechanics
and its formulation as a variational principle. The material should be familiar
to those who have studied mechanics at the undergraduate level.
Because a thorough understanding of this material
is recommended in order to be prepared for the Ph.D. Qualifying Exam, we
will cover it with an emphasis on solving problems.
Chapter 3 covers motion of two bodies interacting by a central force.
This includes classical scattering. There is a nice connection to
semi-classical scattering in quantum mechanics that we will discuss, in
addition to the material in the text.
Chapters 4 and 5 cover rotations of rigid systems.
A recent Qualifier had a problem on rigid-body motion.
Euler angles and rotations also show up in quantum mechanics, where they
are generated by Lie operators. We will discuss the Lie algebra of the
rotation group in addition to the material in the text.
Chapter 6 covers small oscillations. Typical problems
involve choosing suitable coordinates, obtaining the lagrangian
equations of motion, and then solving for the normal modes of vibration.
Symmetery plays an important role in seeing what normal mode vibrations
are allowed.
These general techniques should be mastered for Qualifier preparation.
Chapter 7 introduces the special theory of relativity.
This is a major change for the 3rd Edition because
it uses the standard Minkowski metric. Emphasis will be on using Lorentz
invariance to relate things in different frames. I do not plan to cover 1-forms or to introduce the general theory of relativity.
Ch. 8 covers the hamiltonian form of mechanics. This is the form that is used
in developing quantum mechanics and it is important to understand how to
get a classical hamiltonian as that allows the quantum mechanical hamiltonian to
be obtained by a straightforward procedure.
Chapters 9-10 contain more specialized topics that help one to appreciate the
the connection between classical and quantum mechanics. This course will
provide a brief discussion of canonical transformations and a brief
discussion of Hamilton-Jacobi theory for scattering by a central force.
Chapter 11 is new in the 3rd Edition. We will cover it as an introduction to Chaos.
Chapter 12 will not be covered.
Chapter 13 is often referred to as
classical field theory. It develops the generalization
of particle mechanics to continuous systems.
The number of degrees of freedom in a continuous system is infinite
because each infinitesimal piece
of the system is treated as a particle. The label for an infinitesimal
particle is its
position x, and the displacement of the particle is a function q(x).
(This notation replaces the index i and displacement x for each discrete particle.)
These are essentially bookeeping changes but they lead to
a lagrangian formulation of mechanics for the classical field q(x).
Equations of motion for the field q(x) are typically wave equations.
Essentially the same procedure is used in quantum field theory.