Physics 451: Classical Mechanics

Physics 451: Classical Mechanics Class: Tuesday & Thursday, 12:35-1:55 from January 5 to April 13. There will be no class Feb 23 or Feb 25. Although the official location is MCMED 1345 I have reserved the board room (ERP 104) for the rest of the semester, so the class will take place there instead. Instructor: Alex Maloney • [email protected] Rutherford Physics 316, (514) 398-1417 • Office Hours: Thursday 2-3pm or by appointment. TAs: Loison Hoi & Julien Lhermitte • [email protected] Rutherford Physics 306, (514) 398-6514 • [email protected] Rutherford Physics 422, (514) 398-7033 • Office Hours/Tutorial: Friday 2-3pm in the Piano Room (ERP 211) or by appointment. Communications: • Announcements will be sent to registered students at their mcgill.ca email address. Contact me if you are not registered and would like to get course announcements. • Lecture notes, recordings of lectures and assignments will (technology permitting) be posted on the course webpage: http://www.physics.mcgill.ca/~maloney/451/. I can not guarantee that I will record every lecture. • A link to last year’s lecture notes and recordings is posted on the webpage. This year’s class will differ slightly but the notes may be helpful if you wish to have them in front of you during class. Grading:12 Your grade will be be dropped.



3 Homework 10



+ 15 Midterm + 12 Final . Your lowest problem set grade will

• Midterm: held during class at a date to be determined, most likely Feb 11, 16, or 18. It will be a closed book exam (no texts or notes allowed). • Final: held during exam period at a date and time to be determined. It will be a closed book exam (no texts or notes allowed). • Homework: problem sets assigned more or less weekly. They will be handed out in class and posted on the course webpage shortly afterwards. They will be due roughly one week after they are assigned; solutions should be placed in the TA’s physics department mailbox before the due date. You are encouraged to discuss these problems with your colleagues, but you must write up your own solutions. 1

McGill University values academic integrity. Therefore, all students must understand the meaning and consequences of cheating, plagiarism and other academic offences under the Code of Student Conduct and Disciplinary Procedures (see www.mcgill.ca/integrity for more information). 2 In accord with McGill University’s Charter of Students Rights, students in this course have the right to submit in English or in French any written work that is to be graded.

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The solutions you hand in should reflect your own work and understanding. If you need an extension, contact me or a TA before the due date. Prerequisites: Introductory Mechanics at the level of Kleppner & Kolenkow. Multivariate calculus, differential equations and linear algebra at the level of Apostol. Some exposure to electromagentism and quantum mechanics is useful but not strictly necessary. Text: Hand & Finch, “ Analytical Mechanics.” Available at Paragraphe books (2220 Av. McGill College). It is also on reserve at Schulich library. This text is pretty good: the material is well chosen, presented in modern notation and at an appropriate level. Recommended Reading: • Kleppner & Kolenkow, “An Introduction to Mechanics.” Review of elementary mechanics. • Marion & Thornton, “Classical Dynamics of Particles and Systems.” Alternative text, containing most of the material we will cover but at slightly lower level. • Goldstein, “Classical Mechanics.” Standard graduate text, containing essentially the same material we will cover but at a slightly higher level. • Landau & Lifshitz “A Course on Theoretical Physics: Mechanics.” A classic, containing essentially the same material we will cover but in an idiosyncratic Russian style. Highly Recommended! • Arnold, “Mathematical Methods of Classical Mechanics.” A mathematical classic. Somewhat tangential to the focus of this course. Outline: • Degrees of freedom. Lagrangian Mechanics. Energy and Momentum. (Ch. 1) • The Calculus of Variations. Euler-Lagrange equations. Lagrange multipliers. (Ch. 2) • Small fluctuations. Oscillators: simple, damped and forced. (Ch. 3) • Symmetries and Conservation laws. Noether’s theorem. (Ch. 5.1 – 5.2) • One dimensional systems. (Ch. 4) • The two body problem. Motion in a central field. The Kepler problem. (Ch. 4) • Midterm: Covers material up to and including section 5.2. • Non-inertial and rotating coordinate systems. Fictitious forces. (Ch. 7) • Rigid Bodies. Euler’s equations. (Ch. 8) • Theory of small fluctuations. Normal Modes. (Ch. 9) • Hamiltonian Mechanics. Phase space. (Ch. 5.3 – 5.7) • Poisson Brackets. Canonical Transformations. Symmetries. Noether’s theorem. (Ch. 6) • Advanced Topics: Liouville’s theorem & Poincar´e recurrence. Hamilton-Jacobi theory. Quantization. Integrable systems. • Final: Covers all material except Advanced Topics. 2