2018 SPRING PHYS 8011 Classical mechanics I (as of Apr. 19/2018) The course syllabus is a general plan for the course; deviations announced to the class by the instructor may be necessary. A FRIENDLY REMINDER: Physics is difficult, and it has a very steep learning curve. The learning process can be frustrating and nonlinear. Often you have to work for a long time, many days and even weeks, without feeling that you are making much progress. Then, suddenly, everything falls into place and it all makes sense. But until the click, you can t be sure how much time you d need to get it and it s difficult to plan. As you solve a physics problem, stop and ask yourself: What exactly are you doing? Why are you doing it? How does it help you? Please see my suggestions on how to do well in this class in the table below. To remind ourselves why we do physics, click here: https://en.wikipedia.org/wiki/history_of_physics Course Description: The mechanics of particles and rigid bodies is developed using generalized coordinates, D'Alembert's principle and Hamilton's principle. Symmetry principles and conservation laws are emphasized. Your Objective: To learn how to do physics Athena Title: CLASSICAL MECHAN I Prerequisite: PHYS 4102/6102 Corequisite PHYS 8401 Grading System: A-F (Traditional) Instructor: Dr. Andrei Galiautdinov Office: 220 Email: ag@physast.uga.edu Web & Slides https://www.physast.uga.edu/research/ag/phys8011-graduate-classical-mechanics Sections: 27362 09:30a - 10:45p TR Office hours: 03:15p - 04:15p TR [or, by a verbal appointment, after the departmental colloquium, if there is one on Thursday; takes place in the auditorium (Rm. 202), usually ends at 4:35p] Main Text: In-class notes Useful texts: I. L. D. Landau & E. M. Lifshitz, Course of Theoretical Physics, Vol. 1, Mechanics, 3 rd edition (Elsevier, Butterworth Heinemann, 1976). E-journals access: Academic Honesty: Attendance: Homework assignments: Quizzes: II. H. Goldstein, C. P. Poole, J. L. Safko, Classical Mechanics, 3 rd edition (Pearson, 2002). http://www.libs.uga.edu/ejournals/ As a University of Georgia student, you have agreed to abide by the University s academic honesty policy, A Culture of Honesty, and the Student Honor Code. All academic work must meet the standards described in A Culture of Honesty found at: www.uga.edu/honesty. Lack of knowledge of the academic honesty policy is not a reasonable explanation for a violation. Questions related to course assignments and the academic honesty policy should be directed to the instructor. Mandatory Should be viewed as take-home exams; will be used as preparation for the quizzes. One HMWK problem chosen at random at start of class. Closed notes, closed book A simple (non-graphing, non-symbolic, non-programmable) scientific calculator No other electronic device(s) permitted Must work individually (unless permitted otherwise) Attention: The actual number of quizzes may be different.

Grading policy: -1% FOR EACH ABSENCE 90% MIDTERM QUIZZES (at start of class for 15 20 minutes; one problem chosen at random from assigned homework; no make-ups; worst quiz will be dropped) 10% FINAL EXAM (cumulative, mandatory, no make-up) Cut-offs: F: [0, 60) D: [60, 68) C-: [68, 70) C: [70, 75) C+: [75, 78 ) B-: [78, 80) B: [80, 85) B+: [85, 88) A-: [88, 90) A: [90, 100] NOTE: No rounding; 89.99 = A-, etc. Grades: Your grades will be posted on the elc-new, http://elcnew.uga.edu How to do well in this class: 1. Start working from Day One. 2. Attend every lecture. 3. Take good notes. 4. Ask questions. 5. Participate actively in discussions. 6. Do not shy away from a debate. 7. Re-read and re-work the notes carefully after class. 8. Do homework as soon as it is assigned. 9. Concepts first. Do NOT plug-and-chug. 10. Use a buddy system: find a friend with whom to discuss physics. 11. Form a study group. 12. Teach physics to others. 13. If you like competition, form several groups competing with each other. 14. Finally, think about physics on a regular basis. 15. If everything fails, drop the class before the deadline and re-take it at a later time. 2018 Spring Schedule ATTENTION: The number of quizzes, as well as the quiz dates, may change. NOTE: The following is the minimal amount of material I plan to cover, assuming the slowest pace in the course, so this schedule is very preliminary and is subject to significant change. As a graduate student, you should read additional portions of the recommended textbooks in your spare time. Week Day Date Topic R Jan. 04 Part 1: Kinematics Intro to this course F Jan. 05 1 M Jan. 08 T Jan. 09 Kinematics of a point mass Inertial reference frames Cartesian coordinates W Jan. 10 D r o p/a d d e n d s R Jan. 11 Kinematics in curvilinear coordinates Example: spherical coordinate system F Jan. 12 M Jan. 15 M L K D a y T Jan. 16 Quiz 01: Kinematics 2 Part 2: Newtonian Dynamics Newton s Second Law of motion in curvilinear coordinates (Case 1: Potential Forces) The Lagrangian Brief review: conservative vs. non-conservative forces, potential energy Example: Point mass subjected to uniform gravity (to be finished at home) W Jan. 17 R Jan. 18 NO CLASS F Jan. 19 M Jan. 22

3 4 5 6 7 T Jan. 23 Newton s Second Law of motion in curvilinear coordinates (Case 2: Generallypotential forces) Example: Charged particle subjected to the electromagnetic field W Jan. 24 R Jan. 25 A comment on the Lagrangian (non-uniqueness) Newton s Second Law of motion (for a material point) and the operational definitions of acceleration, force, and mass. Conceptual discussion F Jan. 26 M Jan. 29 T Jan. 30 Newton s Second Law: The three simplest cases W Jan. 31 R Feb. 01 Part 3: Lagrangian mechanics with constraints Mechanical systems with constraints Spherical pendulum as a motivational example Types of constraints Particle constrained to a uniformly moving plane F Feb. 02 M Feb. 05 T Feb. 06 Quiz 02: Newtonian & Lagrangian Mechanics (without constraints) Actual, possible, and virtual displacements Ideal constraints Ideal rod as an ideal constraint W Feb. 07 R Feb. 08 Lagrange equations of the 1 st kind F Feb. 09 M Feb. 12 T Feb. 13 Degrees of freedom & generalized coordinates d Alembert Lagrange equations Derivation of the Lagrange equations of the 2 nd kind Generalized force The case of generally-potential forces Lagrangian W Feb. 14 R Feb. 15 Lagrange equations of the 2 nd kind Configuration manifold F Feb. 16 M Feb. 19 T Feb. 20 Quiz 03: Lagrange equations of the 1 st kind; Integration of the equations of motion Generalized momentum The Law of Change of Generalized Momentum The Law of Conservation of Generalized Momentum Some examples: Free particle in 3D space; particle in 3D space subjected to uniform gravity Generalized energy function (to become the Hamiltonian) The Law of Change of Generalized Energy The Law of Conservation of Generalized Energy Example: Point charge subjected to an EM field Some remarks on kinetic energy W Feb. 21 R Feb. 22 Part 4: Hamiltonian dynamics Hamilton s (canonical) equations of motion

8 9 10 11 12 F Feb. 23 M Feb. 26 T Feb. 27 Point mass in 3D in spherical coordinates (summary) The central force problem Qualitative example 1: weakly singular attractive potential W Feb. 28 R Mar. 01 A remark on closed orbits (Bertrand s Theorem) Qualitative example 2: strongly singular attractive potential Qualitative example 3: repulsive potentials (DIDN T COVER) Conic sections (review) F Mar. 02 M Mar. 05 T Mar. 06 Quiz 04: Lagrange equations of the 2 nd kind Equations of various curves in polar coordinates Conic sections (review cont.) The Kepler Problem W Mar. 07 R Mar. 08 The Kepler Problem (cont.) Kepler s Equation Kepler s 3 rd Law F Mar. 09 M Mar. 12 T Mar. 13 W Mar. 14 S p r i n g B r e a k R Mar. 15 F Mar. 16 M Mar. 19 W i t h d r a w a l d e a d l i n e T Mar. 20 The Two-Body Problem W Mar. 21 R Mar. 22 Poisson Brackets F Mar. 23 M Mar. 26 T Mar. 27 Dirac s quantization conditions Part 5: Small oscillations 13 14 Rayleigh s Dissipation Function W Mar. 28 R Mar. 29 The Principle of Virtual Work 1D Oscillations F Mar. 30 M Apr. 02 T Apr. 03 Quiz 05: Hamiltonian dynamics; Poisson Brackets 1D Oscillations: Examples W Apr. 04 R Apr. 05 Forced 1D Oscillations with and without Dissipation F Apr. 06 M Apr. 09 T Apr. 10 Part 6: N-dimensional oscillations Two degrees of freedom: Free oscillations W Apr. 11 R Apr. 12 Quiz 06: 1D Oscillations Normal modes

15 Multi-dimensional oscillations F Apr. 13 M Apr. 16 T Apr. 17 Part 7: Non-inertial frames Motion relative to a non-inertial frame of reference W Apr. 18 R Apr. 19 Quiz 07: Multi-dimensional Oscillations F Apr. 20 M Apr. 23 16 T Apr. 24 (cont.) Non-inertial frames: Lagrangian & Hamiltonian formulations W Apr. 25 C l a s s e s E n d R Apr. 26 R e a d i n g D a y F Apr. 27 M Apr 30 17 T May 01 W May 02 R May 03 FINAL EXAM: 08:00a 11:00a F May 04 Commencement 18 M May 07 Grades due (5 PM) T May 08 W May 09 R May 10 F May 11 M May 14 19 T May 15 Spring Semester 2018 Based on 50 minutes classes (MWF), 75 minutes classes (TTH), 15 weeks of classes + Exams Orientation/Advisement Jan. 2 Jan. 3. Tuesday Wednesday *Confirmed Registration Jan. 3 Wednesday Classes Begin Jan. 4 Thursday Drop/Add for undergraduate and graduate level courses Jan 4-10 Thursday - Friday; Monday - Wednesday Holiday: Martin Luther King Jr. Day Jan. 15 Monday Midterm Feb. 26 Monday Last Day of Classes Prior to Spring Break March 9 Friday Spring Break March 12 16 Monday Friday Classes Resume March 19 Monday Withdrawal Deadline March 19 Monday Classes End April 25 Wednesday Reading Day April 26 Thursday Final Exams April 27; April 30 - May 3 Friday; Monday - Thursday Commencement May 4 Friday Grades Due May 7, 5 PM Monday, 5 PM