Overview
This course offers an introduction to classical mechanics, continuing the development of concepts introduced in 171.105, however, treating many topics from a more advanced perspective. The course starts with the Lagrangian mechanics,an alternative approach to Newtonian mechanics which is frequently more powerful. Next the potential and kinetic energy are reviewed, and the conservation laws are examined from the point of view of the Lagrangian. The course continues with central foce motion, rigid body dynamics, and oscillations (for a single particle and a coupled system). The Hamiltonian mechanics brackets the other end of the course, paving a way towards the transition to quantum mechanics.
News
Books
The textbook for the course is
The following two books are also good and can be found in the library:
Syllabus and Homeworks
Notation for the reading: "T" means "Taylor", "LL" means "Landau & Lifshitz", the number is the chapter number. All problems are from Taylor (except when otherwise noted), so only the problem number (in the format (chapter.problem)) is given.
| Week of | Lectures (Mon, Wed, Fri) | Reading | Homework (due the following week on Friday) |
| Jan. 28 | Intro, Diagnostic Midter, Calculus of Variations | T-6 |
6.1, 6.2, 6.4, 6.6, 6.10, 6.14, 6.20 |
| Feb. 4 |
Lagrangian Mechanics |
T-7, LL-1 | 7.3, 7.5, 7.9, 7.13, 7.14 + Examples 7.5, 7.6 and 7.7 done with forces |
| Feb. 11 | Lagrangian Mechanics |
T-7 LL-2 | 7.16, 17, 20, 21, 22, 23, 25, 27 (solutions, parts I, II, III) |
| Feb. 18 | Conservation Laws, Lagrange multipliers (extra lecture on Thursday) |
T-7, LL-2 | 7.29, 30, 32, 34, 45, 48, 50, 51, 52 (solutions I, II, III, IV, V) |
| Feb. 25 |
Gravity, Central force-fields (Petar @ CERN, conferences on Mon, Wed in class -- prep for midterm, Fri as usual) | T-8, LL-3 |
8.2, 3, 5, 7, 8, 10, 12, 13 (solutions) |
| Mar. 3 |
Motion in a central force-field First Midterm (covering up to gravity) on Friday March 7, 9 am (in class) |
T-8, LL-3 |
8.14, 15, 20, 21, 22, 23, 29, 31 (solutions) |
| Mar. 10 | Kepler orbits, System of particles (review), collisions, cross-sections |
T-8, 14 |
8.32, 8.35 14.1, 7, 9, 13, 14 (Due Fri March 28) (solutions I, II) |
| Mar. 17 | (Spring Break) |
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| Mar. 24 | Rutherford scattering, System of particles, Rotation about fixed axis, moments and products of inertia. |
T-14, T-10 | Class HW #1, 10.1, 2, 4, 5, 6, 7, 9, 11 (solutions) |
| Mar. 31 |
Rigid body dynamics: angular momentum of an arbitrary rotation, intertia tensor. |
T-10 |
10.19, 20, 21, 22, 24, 25, 27, 28, 33 (double credit! Hint: check Landau) (solutions) |
| Apr. 7 |
Newton's laws in rotating frame. Euler equations, spinning tops. Euler angles. |
T-10 (T-9) | 10.29, 30, 31, 32, 34, 35, 36, 37, 38 (double credit!) (solutions) |
| Apr. 14 | Oscillations: free, damped, forced, resonance. Second Midterm (covering central force orbits and rotation) on Friday April 18, 9 am (in class) |
T-5 | 5.4, 12, 18, 25, 27, 30 (solutions I, II, III) |
| Apr. 21 | Forced oscillations, resonance. Coupled oscillators and normal modes. Hamiltonian Mechanics (intro). (Additional lecture on Thursday Apr 24 1:30) |
T-5, T-11, T-13 |
5.41, 43 5.46, 47, 48 11.14, 19 |
| Apr 28 |
Hamiltonian Mechanics |
T-13 | 13.4, 5, 11, 12, 14 Extra credit: 13.18. (Due Friday 4:30 pm in Petar's mailbox.) Practice final (counts as a whole homework) (due Wed May 7 in review session.) |
Logistics
Grade-computation algorithm: There will be two midterms and one final exam. The final grade will be based 20% on the homework, 25% on the midterm with a higher score, 15% on the other midterm, and 40% on the final exam. (If a midterm is missed, a running homework average minus 30% is used instead.)
Lectures: Mon-Wed-Fri 9:00-9:50am, in Bloomberg 168.
Conference: Thu 1:30-2:20pm, also in Bloomberg 168.
Office hours: being discussed.
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Instructor: |
Petar Maksimovic |
TA: |
Chris Eskew |
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Email: |
Email: |
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Room: |
Bloomberg 417 |
Room: |
Bloomberg 421 |
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Phone: |
6-3819 |
Phone: |
6-5106 |
URL: http://www.pha.jhu.edu/courses/171_204/
