Subject:
Graduate Classical Dynamics
Number: PHGN 505
Course Title: Classical Mechanics I
Section: A
Semester/year: Fall 2014
Instructor or Coordinator: Prof. Lincoln Carr
Contact information (Office/Phone/Email): Meyer Hall 342, 303-273-3759, lcarr@mines.edu
Office hours: M 2-4, W 1-4
Class meeting days/times: MWF 4-5 pm
Class meeting location: Meyer Hall 363
Web Page/Blackboard link (if applicable): http://inside.mines.edu/~lcarr Teaching Graduate Classical Mechanics, Physics 505
Teaching Assistant (if applicable): TBA
TA Contact information (Office/Phone/Email): TBA
Instructional activity: _3_ hours lecture
_0_ hours lab
_3_ semester hours
Course designation: ___ Common Core ___ Distributed Science or Engineering
___ Major requirement ___ Elective _X_ Other (Graduate core)
Course description from Bulletin: Review of Lagrangian and Hamiltonian formulations in the
dynamics of particles and rigid bodies; kinetic theory; coupled oscillations and continuum
mechanics; fluid mechanics.
Textbook and/or other required materials:
Required texts:
1. Theoretical Mechanics of Particles and Continua, Fetter and Walecka
2. Nonlinear Mechanics: A Supplement to Theoretical Mechanics of Particles and Continua,
Fetter and Walecka
Supplemental texts (you do not need to purchase these books):
1. Mechanics, Third Edition, Landau and Lifshitz volume I
2. The Classical Theory of Fields, Fourth Edition: Volume 2 (Course of Theoretical Physics
Series), L. D. Landau and E.M. Lifshitz
3. Classical Mechanics, Third Edition, Goldstein, Poole, and Safko
4. Mathematical Methods of Classical Physics, Second Edition, Arnold (advanced)
In addition there is a lower level text which is recommended for review of undergraduate
material:
5. Classical Mechanics, John R. Taylor
Student learning outcomes: At the conclusion of the class students will…
1. Understand and be competent in concepts associated with research in classical dynamics
up through recent research advances.
2. Understand and be competent in analytical calculations associated with research in
classical dynamics up through recent research advances
3. Have gained an improved ability to choose and apply numerical methods towards solving
research problems.
4. Have completed an introductory research project useful towards her/his thesis research
in its methodology.
Note: Student learning outcomes are focused on building research skills towards
eventual completion of graduate thesis work.
Brief list of topics covered:
1. Newtonian Mechanics, Conservation Laws, Central Force Motion, Hyperbolic Orbits,
Scattering
2. Accelerated and Rotating Reference Frames, Motion on the Surface of the Earth
3. Generalized coordinates, d'Alembert's principle, Lagrange's equations of motion
4. Calculus of variations, Hamilton's principle, Lagrange multipliers, Generalized Momenta,
Hamiltonian
5. Normal mode analysis, leading to many body theory
6. Discrete to continuum limits and a first look at classical string theory
7. Inertia tensor, Euler's equations, and Applications
8. Hamilton's equations, canonical transformations, action-angle variables, and Poisson
brackets
9. Duffing oscillator, Phase space dynamics and fixed points, Action-angle variables, Planar
pendulum
10. Linearized stability analysis, Lorenz model, Continuum chaos, Lyapunov exponent,
Strange attractor
11. Logistic map, Period doubling route to chaos, Feigenbaum numbers
12. Liouville's theorem, Action-angle variables Take II, Separability, Integrability, Poincare
section
13. Perturbation of Hamiltonian systems, Resonant disruption of phase space
14. Case study of resonant disruption of 4D phase space for coupled pendula, KAM theory
Grading Procedures:
1. Final Grade
•
Weekly homeworks: 50%
•
Mid-term: 25%
•
Final: 25%
2. This class is graded on a modified curve. Any modifications can only be upwards, and
must be applied uniformly. That means, for example, that I can set a cut for a B lower
than strictly dictated by the laws of statistics, but I will never set it higher. The mean is
initially set at a GPA of 3.3, or a B+, as is standard for graduate courses. I will use +/grading.
3. Homework will normally be collected at the beginning of the Friday class session. The
course policy on unexcused late homework is as follows:
•
1 day late: 25% credit removed for lateness
•
2 days late: 50% credit removed
•
3 days late: 75% credit removed
•
4 days late: automatic grade of zero.
a. “1 day late” is defined as any time after the due date and time of Fridays at 4:00
p.m. This includes one minute late. The course policy is quite strict in this regard.
Note that I hand out all assignments at least a week in advance. Please plan ahead
so you do not get yourself in such a situation. This is a no-exceptions policy for
unexcused absences. Weekends and holidays do not count as late days.
b. Why be so strict, you may ask? The reason is that’s how the world works outside
graduate school and in professional life. E.g. if I submit a grant proposal to NSF,
one minute late is too late, and the system rejects my proposal automatically. Our
job is to prepare you to be professional physicists. I therefore try to replicate the
world outside graduate school as much as possible.
4. Homework will be scored according to its expected difficulty. Thus in some weeks
homework will be worth more than others.
5. I do not give incompletes under any circumstances excepting documented life-threatening
situations such as extended hospital stays for cancer treatment or other major illnesses.
Coursework Return Policy:
Graded homework and exams will be returned within two weeks unless otherwise stated, in
which case the reason will be explained clearly to the class (e.g. TA/lecturer attending a
professional conference etc.) Feedback on your assignments will be provided and the lecturer
and TA are both available during office hours to consult regarding your homework.
Absence Policy (e.g., Sports/Activities Policy, or attending a professional conference associated
with your research):
• If you are going to miss class for a scheduled reason, you must clear it with me ahead
of time. I will ask you to provide clear evidence of your conference or other activity, and
such activities must be approved by the instructor in writing in advance.
• If you are sick and will miss class due to your illness, email me in advance.
• Homework must be turned in before it is due to be graded – plan ahead.
• Exams: If you will be absent during a scheduled exam, you must schedule a make-up
time before you leave.
Homework:
Analytical problem sets will normally be assigned on Friday and will be due the following
Friday at the beginning of class, 4:00 p.m., with rare exceptions. Information on research
projects is contained in associated problem sets on the course webpage.
Exam Policy:
1. There will be one midterm and one final.
2. Exams are cumulative.
3. The midterm and final are weighted equally. Both are two-hour exams.
4. Exams are completely low-tech – no computational devices, calculators, cell phones, or
even slide rules. You should avoid overuse of computational aids to solve analytical
homework problems, as this will cause you to perform poorly on exams.
5. On the day of an exam you are permitted to bring only pencil and paper – no cell phones,
backpacks, etc. If you have nowhere to put your personal effects, you can leave them in
my office by showing up early to class.
6. If you need extra time for exams due to a learning disability, please come let me know
right away so I can make arrangements for you. Please provide proper CSM certified
paperwork.
Detailed Course Schedule:
This information is found on the course webpage.
Course representatives:
You will elect two course representatives by the end of the first week of classes. You are of
course welcome to come speak to me about any aspect of the course at any time. In addition I
will meet weekly with course representatives during office hours about all aspects of the course.
You can expect course representatives to poll you on a weekly basis on any issues that may arise,
e.g. timing and content of homework, pace and style of the lectures, etc.
Important Class Policies:
1. I expect all students to attend every class.
2. I will expect you to function as researchers and treat you as professionals. This means if
you don’t understand something, you should be reading the recommended texts for the
course and coming to office hours on your own initiative.
3. A basic knowledge of undergraduate classical mechanics, such as one finds in Taylor’s
book (see above), is expected. Likewise this course requires a knowledge of
mathematical physics as covered in PHGN511 (concurrent with the course) and a basic
understanding of Lagrangian and Hamiltonian formalism as covered in intermediate
mechanics PHGN350. This does not mean you are the world’s expert on these topics. But
you should have either taken these classes, passed them, and retain some basic
understanding, or you should get textbooks and teach yourselves as needed. I enjoy these
topics very much and will be happy to review them during office hours, but will not
cover them in any depth in class.
4. Copies of class notes will be provided for you, either via the web or in hard copy form.
Make sure to check the web the evening before class. Have a hard or soft copy of the
notes on your desk when you attend class. The main reason I provide you with my notes
is so that, instead of spending your time copying from the board, you can think about the
material as it is presented.
5. I will expect you to read the book before lecture, as assigned. I will not present every
detail of every subject in class. The midterm and the final will cover both the text and the
lecture notes, as well as all homework and solution sets. Therefore, you should plan to
study the text thoroughly.
6. I will expect you to learn both concepts and calculation methods. Conceptual questions
will count for a good portion of each exam, typically about a quarter of the available
points. The focus is on understanding, not on solving canned problems – though of course
you should know how to do the latter, too.
7. My personal take on academic integrity, in addition to the required formal CSM policy
statement given at the end of this syllabus, is the same as you would find in a research
journal or with e.g. the National Science Foundation. Plagiarism of any kind will not be
tolerated. If you use a source, you must quote it. Working together on homework is
permitted, but the majority of your work should be individual. A near verbatim copy of
another student’s homework counts as plagiarism. Use of internet material or any other
media without citation is plagiarism. For the purposes of this course, this includes noncopyrighted material. Any suspected plagiarism cases will be referred to the Dean of
Students for disciplinary action, without exception.
8. I prefer personal contact to e-mail contact, and therefore encourage you to come to office
hours. If you can’t make my office hours, we can try to make a special appointment. In
this case, please notify me at the conclusion of the lecture hour, at least one day before
you wish to meet with me. I check my e-mail once per day, usually by 5:00 p.m., Monday
through Friday, and typically get over 100 e-mails per day, resulting in a long delay time
for responses. As a rule, I do not address homework problems by e-mail. On the other
hand, if you need to let me know about a personal emergency, e-mail is fine.
9. Cell-phones and other electronic devices should always be off in class, and should not
appear at any time during lecture. Use of electronic devices for e-mail and other tasks
during class will lead to poor performance (cognitive science studies have shown that the
human mind is spectacularly bad at multi-tasking). Repeated violation of this policy will
lead to my asking you to no longer attend lectures. Use of an electronic device to read a
soft copy of the notes is of course encouraged. Any kind of frequent typing or continual
swiping of screens during class will lead to my asking you to no longer attend lectures.
a. An exception can be granted under special circumstances and should be discussed
with me in person in advance; e.g., if you are a parent with a young child in
daycare you may need to leave your phone on in silent mode.
10. You are always welcome to come speak with me during office hours about physics and/or
general science topics outside the course material.
11. There are occasionally research positions in the CTPRG (Carr Theoretical Physics
Research Group). If you become interested in this possibility, please don’t hesitate to
come talk to me about it.
Suggestions:
1. Work hard from the very beginning. If you find it easy at first then read ahead. It will get
difficult rapidly. We will go at a fast pace. This is an indication of my confidence in your
dedication and ability as up-and-coming scientists.
2. If you have difficulties, see me right away. Do not wait until you are completely lost and
there is no hope of catching up. Everything will only get more and more difficult. You
cannot afford to not understand any concept. In physics every new concept relies
crucially on the previous ones.
3. Interrupt me in class and ask lots of questions. Remember that if you do not understand
something, chances are neither do most of your classmates. If you don’t ask questions, I
will assume that you all understand perfectly and continue at a fast pace. Remember, the
main difference between you and me is I’ve made more mistakes. Don’t be shy. Ask
questions. There are no stupid questions.
4. Don’t let the lecturer (me) constrain your learning! Rather, take my lectures as a
springboard for your own interests. Many subjects we cover will be a matter of ongoing
research. If you have doubts about the veracity of what I present, you may be the one to
publish the paper that finally gets it right. Write down your doubts and your creative
ideas, and keep a notebook of all such insights for future use in research.
5. The best scientists are not necessarily the ones who got A’s in college and/or graduate
school. The best scientists are the ones who understand the problems they solve and think
about them creatively. So focus more on understanding than on grades. A high IQ and
high grades are not impressive and will not rock the world of science. Creative genius
will. So focus on the latter.
Official CSM policy statement on academic integrity/misconduct:
The Colorado School of Mines affirms the principle that all individuals associated with the
Mines academic community have a responsibility for establishing, maintaining and fostering an
understanding and appreciation for academic integrity. In broad terms, this implies protecting the
environment of mutual trust within which scholarly exchange occurs, supporting the ability of
the faculty to fairly and effectively evaluate every student’s academic achievements, and giving
credence to the university’s educational mission, its scholarly objectives and the substance of the
degrees it awards. The protection of academic integrity requires there to be clear and consistent
standards, as well as confrontation and sanctions when individuals violate those standards. The
Colorado School of Mines desires an environment free of any and all forms of academic
misconduct and expects students to act with integrity at all times.
Academic misconduct is the intentional act of fraud, in which an individual seeks to claim credit
for the work and efforts of another without authorization, or uses unauthorized materials or
fabricated information in any academic exercise. Student Academic Misconduct arises when a
student violates the principle of academic integrity. Such behavior erodes mutual trust, distorts
the fair evaluation of academic achievements, violates the ethical code of behavior upon which
education and scholarship rest, and undermines the credibility of the university. Because of the
serious institutional and individual ramifications, student misconduct arising from violations of
academic integrity is not tolerated at Mines. If a student is found to have engaged in such
misconduct sanctions such as change of a grade, loss of institutional privileges, or academic
suspension or dismissal may be imposed.
The complete policy is online.