Tuesdays and Thursdays at 13:30 - 14:45 Room 202, OCNPS

- Thursdays 4:00 p.m. - 5 p.m. in my office Physical Sciences
Building (PSB II), Room 2100J

- and by appointment (send email or see me after class).

Here is the Final Exam and here is the solution.

You can submit your solutions by scanning them in or typesetting them and sending them via email. Here are some "scanning hints":

- If at all possible, use a scanner, not a camera. Some cell phones have a built-in scanning app (for instance inside "Notes" on the iPhone) which still would be better than just taking a regular photo.
- If you have to use a camera, make sure you have a white background, white paper and black pen to write your solutions, and bright illumination for the photo. Check if the photo is in focus and retake it if not.
- You may have access to some image-enhancement software - if so, please increase the contrast and brightness if your submission is dark or without contrast, and try the sharpening tool. Alternatively, you can let me do those things, but I can do it only if you send .JPG or .png or .tiff files, NOT pdf.

Finally, don't forget about your participation project! Given the new situation, lecture notes (typeset!) or Mathematica notebooks would be best; however, if you want to give a presentation instead, please send the slides to me beforehand so I can post them. Let me know if you need advice or ideas.

Textbooks:

- Required: H. Goldstein, C. Poole and J. Safko: Classical Mechanics – 3rd edition, Addison Wesley 2002
- Optional (if you like a different approach): A.S. Fetter and J.D.
Walecka: Theoretical Mechanics of Particles and Continua (Dover
Publications)

Syllabus

Preliminary Schedule. Note that we will likely have to change the schedule to accommodate the reduced available time. More to follow.

(See Information on Mathematica for help with running notebooks)

N.B.: If my lectures (notes) are too confusing for you, you can also check out Ian Balitsky's and Anatoly Radyushkin's lecture notes. Note that the organization is quite different (following more closely the book by Fetter and Walecka)

Week 1 - Introduction and Lagrangian approach: Whiteboards Lecture 1, Lecture 2, Lecture Notes by R. Dodangodage

Week 2 - Equations of motion, examples and Velocity-dependent potentials: Whiteboards Lecture 1, Lecture 2, Animation Screenshot, Mathematica Notebook, Lecture Notes by AMSD Wijerathna

Week 3 - Hamilton's principle, Lagrangian Multipliers, conserved quantities: Day 1 by Isurumali NETHTHIKUMARA HATHTHELLAGE (Further lecture notes are in the 2nd half of Week 2 above) - Whiteboards Lecture 1, Lecture 2, Mathematica Notebook; Lecture note on conservation laws by Sunil Pokharel.

Week 4 - Central Force Problem, Kepler's Laws: Whiteboards Lecture 1, Lecture 2, Numerics1, Numerics2, Mathematica Notebook1 , Mathematica Notebook2. Also: Summary and Notebook on properties of ellipses and old Lecture Notes by Pushpa Pandey. Also: Lecture Notes by D. Cameron, Another drawing of ellipses. NEW Lecture Notes by H. Pokhrel.

Week 5 - 1.) Continuation of Central Force Problem - Scattering - Whiteboard; 2.) Small coupled oscillations: Whiteboard. Lecture notes by Raj Ghimire.

Week 6 - 1.) Finish coupled oscillations. Whiteboard. Mathematica Notebooks 1 and 2. 2.) Rotations and kinematics of rigid bodies - Whiteboard, 2nd Whiteboard. Older lecture notes.

Week 7 - More on rotations (see Week 6 ). Whiteboards Lecture 1, Lecture 2. Also: Graphic about Inertia Ellipsoid, and web pages 1 and 2 about the first interstellar asteroid (why did I post that?)

Week 8 - Dynamics of rotating bodies. First lecture on Tuesday 3/3 in class, second lecture on Thursday 3/5 for self-study. See previous lecture notes (for both days), including the precession of earth's axis of rotation. Whiteboard for the in-class lecture and older Whiteboards from previous semester for Lecture 1 and Lecture 2. Mathematica Notebook shown in class, for symmetric top with gravitational field, with initial conditions specified in terms of psi-dot, phi-dot and theta. Here are two screenshots from that notebook (you are strongly encouraged to play with it):

- A rotating bicycle wheel, initially with a horizontal axis at rest. You can see how the axis will keep dipping down and back up, with corresponding changes in phi-dot and psi-dot.
- A rotating upright top (with some
tilt relative to the z-axis). You can see how its axis will follow a
"curlicue" pattern, moving (= precessing) "backwards" when the top is
more upright and "forwards" when it is more tilted (nutation).

See also Week 10 on Phase Space. Presentation by A. Coxe on Chaos, Condensed version as presented on Thursday, 3/26.

Week 10 - Phase Space, Canonical Transformations. Whiteboards Lecture 1, Lecture 2. Lecture notes by M. Pokhrel; Animation by J. Frechem Here is the recording of the Tuesday 3/31 Lecture and my presentation . And here is the recording of the Thursday 4/2 Lecture and my presentation .

NOTE: Week 11 - Canonical Transformations - is included in Week 10, so to keep with the original schedule, we'll skip directly to Week 12 for the week of April 6. Here is some more related material: Poisson Brackets. Whiteboards Lecture 1, Lecture 2. Lecture notes by G. Sterling.

Week 12 - ICTs, Poisson brackets, infinite dimensions. Whiteboards: Lecture 1 and Lecture 2. Here is the recording of the Tuesday 4/7 Lecture and Thursday 4/9 Lecture .

Older Whiteboards: Lecture 1, Lecture 2. Lecture Notes by A. Maps

Week 13 - Special Relativity: Intro, Minkowski space, Kinematics. Whiteboards: Lecture 1, Lecture 2. Lecture notes: Lecture 1 , Lecture 2. Recordings: Tuesday 4/14 Lecture ; Password: b1!&5S$? -- Thursday 4/16 Lecture ; Password: c7&4Duy8

Older Whiteboards: Lecture 1, Lecture 2, Old Lecture 1, Old Lecture 2.

Week 14 - Collisions, Lagrangian, Hamiltonian and Electromagnetic interaction in Special Relativity. Tuesday 4/21 Lecture recording -- Password: 0h@538x1 -- and Lecture Notes; Thursday 4/23 Lecture recording ; Password: 6A&sYz$5 . Lecture notes on the electromagnetic field Lagrangian.

Previous year's Whiteboard; Previous year's summary Whiteboard.

HW Problem Set #2 -- Solution #2

HW Problem Set #3 -- Solution #3

HW Problem Set #4 -- Solution #4

HW Problem Set #5 -- Solution #5

HW Problem Set #6 -- Solution #6

MIDTERM EXAM (Take-Home) -- Solution

HW Problem Set #7 -- Solution #7

HW Problem Set #8 - here are the relevant pages from Goldstein et al. -- Solution #8

HW Problem Set #9 - here is again the relevant page from Goldstein et al. -- Solution #9

Final HW Problem Set #10 -- Solution #10