PHY6246: Classical Mechanics

This course is a one semester graduate level course on classical mechanics. The goal of the course is to develop and apply the formulation of Newtonian mechanics by using the canonical variational methods due to Lagrange, Hamilton, and Jacobi. The emphasis will be on the canonical structure of classical mechanics, in which the parallels to quantum mechanics are most transparent. We start with Hamilton's principle of least action to derive Lagrange's equations, and we apply the formalism to dynamical systems with constraints. Conservation of energy, momentum, and angular momentum are linked to symmetry principles. Canonical transformation theory will be developed leading to action-angle variables and the Hamilton-Jacobi equation. We will discuss applications to perturbations about the Kepler solution, small oscillations, and rigid body motion, including the dynamics of tops.

Below are links to course information, a syllabus, a convention and formula sheet. As the course develops, I will be writing lecture notes, which will eventually be posted here.

Required text:

Classical Mechanics , Goldstein, Poole, and Saiko, Third Edition (Addison-Wesley,2002). [errata]

Course Information:

Class and contact Information

Lecturer: Charles Thorn

Lectures: MWF period 3 (9:35-10:25 am), NPB 1101

email: thorn@phys.ufl.edu

Office hours: MW period 5 (11:45a-12:45p), NPB 2069 and by appointment

Our grader: Dipsikha Debnath

email: dipsikha.debnath@gmail.com

Office hours: Tuesdays 11:45a-12:50p, Fridays 5:10p-6:00p, NPB 2044

Announcements, Fall 2013

Homework will generally be due each week at 5pm on Wednesday. It should be handed in either in class on that day or to me in my office before the deadline. See the course information link above for an explanation of penalties for late homework.
Problem set 2 posted 26 August 2013.
Problem set 3 and Solution Set 1 posted 4 September 2013.
Problem set 4 posted 10 September 2013.
Solution Set 2 posted 12 September 2013.
Lecture notes updated 13 September 2013.
Problem set 5 posted 17 September 2013.
Solution Set 3 posted 18 September 2013.
Problem set 6 posted 25 September 2013.
Solution Set 4 posted 25 September 2013.
Problem set 7 posted 1 October 2013.
Problem set 8 posted 8 October 2013.
Solution Set 5 posted 7 October 2013.
Solution Set 6 posted 9 October 2013.
Solution Set 7 posted 18 October 2013. Reminder: the midterm is Wed. 23 October. It will cover topics through small oscillations--no questions on the dynamics of rigid bodies! Relevant homework for the midterm include Problem sets 1-7.
Problem set 9 posted 22 October 2013.
Midterm Statistics: Range: 45-99; average: 77.5; median: 78-79.
Solution Set 8 posted 24 October 2013.
Please note that I have added hints to problem 36 (G, 6.25) in Set 9. I have also made part b) optional since our class discussion of non-holonomic constraints has been minimal.
Problem set 10 posted 30 October 2013.
Problem set 11 posted 4 November 2013.
Solution Set 9 posted 11 November 2013.
Problem set 12 posted 12 November 2013.
Solution Set 10 posted 18 November 2013.
Both Problem Sets 13 and 14 posted 18 November 2013. Because the normal due date for Set 13 is part of Thanksgiving holiday, I am setting its deadline at noon on 2 December. Set 14 will be due by 5 pm on its normal date of 4 December, which is also the last day of classes. That date and time is also the deadline for all late homework. Remember that you can get up to 50% credit on late problem solutions regardless of how late it is.
Solution Set 11 posted 21 November 2013.
UF Online Faculty Evaluations are open from today Tuesday, Nov 26 until Friday, Dec 6. URL for online evaluations: [evaluations.ufl.edu] These evaluations provide very important feedback, so it is essential that we all do our best to maximize the number of responses. You can access the evaluation form at your leisure from the above web site, where you can find instructions and links to a gatorlink login page. It is probably a good idea if you bookmark the page so you can easily find it in the future.
Solution Set 12 posted 2 December 2013.
Solution Sets 13 and 14 posted 7 December 2013.

Homework Assignments

In the homework assignments, I will refer to problems in Goldstein's's book by prefixing the problem number with G.

Problem Set 1, due 28 August 2013, Solution Set 1
Problem Set 2, due 4 September 2013, Solution Set 2
Problem Set 3, due 11 September 2013, Solution Set 3
Problem Set 4, due 18 September 2013, Solution Set 4
Problem Set 5, due 25 September 2013, Solution Set 5
Problem Set 6, due 2 October 2013, Solution Set 6
Problem Set 7, due 9 October 2013, Solution Set 7
Problem Set 8, due 16 October 2013, Solution Set 8
Problem Set 9, due 30 October 2013, Solution Set 9
Problem Set 10, due 6 November 2013, Solution Set 10
Problem Set 11, due 13 November 2013, Solution Set 11
Problem Set 12, due 20 November 2013, Solution Set 12
Problem Set 13, due noon, 2 December 2013. Solution Set 13
Problem Set 14, due 4 December 2013, Solution Set 14
All late homework due 5pm on 4 December 2013.

Information on Examinations

The final exam is scheduled for 12 December 2013, 10:00am-12:00n. The midterm will be given, in class, tentatively on 23 October 2013. In grading the midterm and final exams, points will be deducted for errors in calculation and logic. Both exams will be closed book.

Announcements, Fall 2012

The first week of lecture notes posted 27 August 2012.
Problem Set 2 posted 28 August 2012.
Lecture notes updated 4 September 2012.
Problem Set 3 posted 4 September 2012.
Problem Set 1 is graded and can be picked up in my office, if you want it before Friday.
Solution Set 1 posted 6 September 2012.
PLEASE NOTE: I have decided to push back the due date for Problem Set 3 from 12 September to 19 September 2012. Problem Set 4 will also be due on that date, but it will be quite short (at most 2 problems). The reasons for this change are (1) Problems 11 and 12 rely on concepts that we will discuss in tomorrow's class, and (2) the solution to problem 10 is lengthier than I had originally thought. I hope that the extra time, together with a shortened Set 4, will make the task of completing the assignments easier. Posted 11 September 2012.
Erratum in Set 3: 12. G. Problem 3.19. Note that the approximation alluded to in part b) is the condition $a\gg\rho$. Also the correct answer in this approximation is $\pi\rho^2/a^2$ not the result cited in part b).
Problem Set 4 posted 12 September 2012.
Solution Set 2 posted 12 September 2012. Please note that an error in the rolling w/o slipping constraint in the solution to problem 5 of Set 2 has been corrected, 14 September 2012.
Problem Set 5 posted 19 September 2012.
Lecture notes updated 26 September 2012.
Problem Set 6 posted 26 September 2012.
Solution Sets 3 and 4 posted 27 September 2012.
Problem Set 7 posted 3 October 2012.
We will have an optional discussion every Wednesday afternoon at 5pm. We eill try for the regular classroom.
Solution Set 5 posted 4 October 2012.
The date for our midterm has now been chosen: Friday, 19 October 2012. The exam will cover topics from the beginning of the course through small oscillations and Problem Sets 1-7. No homework will be due on 17 October: Set 8 will be due on 24 October. the exam will be closed book, with any needed formulas supplied in the exam booklet.
Solution Set 6 posted 10 October 2012.
You may peruse the exam formula sheet here
Problem Set 8 posted 16 October 2012.
Solution Set 7 posted 16 October 2012.
Mid term results: Range: 43 - 99, average =81.2, median score=88.
Solution Set 8 posted 31 October 2012.
Problem Set 9 posted 23 October 2012.
Problem Set 10 posted 31 October 2012.
Problem Set 11 posted 7 November 2012.
Lecture notes updated 7 November 2012.
Solution Set 9 posted 7 November 2012.
Problem Set 12 posted 13 November 2012. Note that it is due the day after Thanksgiving break 26 November.
Lecture notes updated 13 November 2012.
Solution Set 10 posted 16 November 2012.
Problem Set 13 posted 18 November 2012.
UF Online Faculty Evaluations are open from Tuesday, Nov 20 until Friday, Dec 7. URL for online evaluations: [evaluations.ufl.edu]
Solution Set 11 posted 21 November 2012.
Problem Set 14 posted 28 November 2012.
Lecture notes updated 30 November 2012.
Solution Set 12 posted 30 November 2012.
End of semester issues: the deadline for all homework, including Set 14 and all late homework is the last day of classes: 5pm, Wednesday 5 December 2012. I will post the solutions to sets 13 and 14 at this time. Any homework problem handed in after this time is eligible for a maximum of 5 points.
Solution Sets 13 and 14 posted 5 December 2012.
Updated Exam formula sheet posted 9 December 2012.
Final exams are now graded and may be picked up in my office. The average and median final exam scores of registered students were 74 and 73 respectively; the range of scores was 47 to 97. As for the total course scores, the average and median total scores of registered students were 78.4 and 81 respectively; the range of total scores was 54 to 94. The grades were: 85-94, A; 80-84, A-; 65-79, B+; 50-64, B.

Homework Assignments

In the homework assignments, I will refer to problems in Goldstein's's book by prefixing the problem number with G.

Problem Set 1, due 29 August 2012, Solution Set 1
Problem Set 2, due 5 September 2012, Solution Set 2
Problem Set 3, due 12 September 2012, Solution Set 3 NOTE NEW DUE DATE: 19 September 2012.
Problem Set 4, due 19 September 2012, Solution Set 4
Problem Set 5, due 26 September 2012, Solution Set 5
Problem Set 6, due 3 October 2012, Solution Set 6
Problem Set 7, due 10 October 2012, Solution Set 7
Problem Set 8, due 24 October 2012, Solution Set 8
Problem Set 9, due 31 October 2012, Solution Set 9
Problem Set 10, due 7 November 2012, Solution Set 10
Problem Set 11, due 14 November 2012, Solution Set 11
Problem Set 12, due 26 November 2012, Solution Set 12, Note new due date!
Problem Set 13, due 28 November 2012, Solution Set 13
Problem Set 14, due 5 December 2012, Solution Set 14

Information on Examinations

The final exam is scheduled for 13 December 2012, 12:30-2:30pm. The midterm will be given, in class, on a date to be determined. In grading the midterm and final exams, points will be deducted for errors in calculation and logic. Both exams will be closed book.