Advanced Mechanics PHY 504 Fall Semester, 2016 (Revised 08/24/16) I. INSTRUCTOR/VENUE Professor Lance De Long Email: lance.delong@uky.edu Office: CP363 (257-4775) Labs: CP75, CP158 (257-8883) Office Hours: M 10:00-11:00 a.m.; T 8:15-9:00 a.m. The Course will meet MWF in CP183, 9:00-9:50 a.m., beginning August 24, 2016. II. COURSE DESCRIPTION/MOTIVATION PHY504 is a three-hour, advanced, lecture and problem course providing a thorough summary of the concepts and formalism of classical mechanics for Physics and Astronomy graduate students and other advanced science or engineering students. The University of Kentucky Bulletin describes PHY 504 as a course that provides a basic description of the classical mechanics of particles and rigid bodies. The Course is a core graduate course for the M.S. and Ph.D. Degrees in Physics and Astronomy, and is at least an implied prerequisite for most advanced graduate courses in Physics and Astronomy. Primary emphasis will be placed on the Lagrangian and Hamiltonian approaches to solving problems in mechanics, including an introduction to variational or path integral formulations that form the foundation of modern field theories. III. REQUIRED MATERIALS AND PREREQUISITES The required textbook is H. Goldstein, C. Poole and J. Safko, Classical Mechanics (Addison Wesley, New York, 2002, 3 rd Edition). A useful reference for path integral techniques is the book by C. Lanczos, The Variational Principles of Mechanics (Dover Publications, 4 th Edition, New York, 1986). The Instructor will put a few other texts or references on reserve in the Chemistry/Physics Library, as announced. There will also be a copy of the lecture notes (as amended on a semi-regular schedule) on reserve in the CP Library. The official prerequisite courses are PHY 404G (Intermediate Mechanics) and MA 214 (which implies that familiarity with multivariate calculus, differential equations and partial derivatives will be essential). The Course will also assume students are familiar with the elementary principles of electricity and magnetism, thermal physics and basic quantum mechanics, at least at the levels of PHY 231, 232 and 361. Additional background covered in PHY 416, 417, 520 and 522 will be very helpful. IV. STUDENT RESPONSIBILITIES The Course Instructor will emphasize active involvement in class discussion, and the use of logic and integrative thinking on the part of the student. Additional out-of-class preparation and
PHY 504 Syllabus 2 Fall, 2016 careful attention in Lecture will be necessary for students to learn important (often subtle) physical concepts, and to help them ask productive questions during class time. Students should also read relevant sections of the textbook or other references (held in Reserve in the CP Library, for example) before they are covered in Lecture. Homework exercises will develop the skills needed to independently apply the information gained in the text and Lecture, and from previously assigned problems, to new situations. Homework problems will be assigned from lecture and the textbook. The student can expect around four or five problems assigned per week, with each problem worth 4 points of credit: 0 pts. for no work turned in; 1 pt. for a poor effort; 2 pts. for a modest effort; 3 pts. for a substantially correct answer; and 4 pts. for an excellent solution without significant error. NOTE BENE: 1) Past experience has shown that poor homework performance is highly correlated with a low course grade. 2) Students should expect to regularly attend class and to spend around 12 hours per week on homework and background reading. V. GRADING The criteria for assigning course grades is contained in the University of Kentucky Bulletin. Note that Graduate Students must maintain minimum grade point averages that differ from the Undergraduate rules; in particular, a C grade is considered a poor performance for Graduate Students. Consult the Graduate School Bulletin for details. The final course grade will be based on: A. Homework (total of scores), 30% B. One Midterm Hour Exam, 30% (to be held in CP183 on Friday, October 14) C. Final Exam, 40% (to be held in CP183 on Monday, December 12, 10:30 to 12:30) The Course Evaluation window will be open Wednesday, November 23, to Wednesday, December 14, 2014. It is mandatory for enrolled students to complete an evaluation of this Course during that period. A list of students who have completed or not completed the evaluation is sent to the Instructor to facilitate the completion of this survey. VI. ATTENDENCE AND MAKE-UPS Please note that students who do not attend either of the first two Lectures of the Course may be dropped from the Course, as demanded by the UK Registrar. If you must miss an examination or cannot turn in a homework set, a make-up can be arranged. Acceptable excuses include serious illness, official University activity (e.g., away game, field trip), etc. Foreseeable absences, such as University activities, must be cleared with your instructor at least one week in advance. Unforeseen absences must be excused by your Instructor no later than one week after the fact in order for a make-up to be allowed. You may not double-schedule classes or agree to out-of-class exams in conflict with PHY 504 exams -- these are not acceptable excuses. The Instructor has the right to request some form of documentation justifying student absences, and has authority to judge the acceptability of the excuse, consistent with University rules.
PHY 504 Syllabus 3 Fall, 2016 In extraordinary circumstances in which the student has a valid excuse for missing a large number of assignments or the Final Exam, an "Incomplete" grade may be given, consistent with University regulations. VII. RECOMMENDED REFERENCES (RESERVE LIST) 1. ( G ) H. Goldstein, C. Poole and J. Safko, Classical Mechanics (Addison-Wesley Publishing, San Francisco, CA, 3 rd Edition, 2002). 2. ( L ) C. Lanczos, Variational Principles of Mechanics (4 th Edition, Dover Paperback) 3. ( LL ) L. D. Landau and E. M. Lifshits, Mechanics (Addison-Wesley Publishing, Reading, MA, 1960). 4. ( M ) J. B. Marion and S. T. Thorton, Classical Dynamics of Particles and Systems (Harcourt, Brace, Jovanovich, San Diego, CA, 4 th Edtion). 5. ( S ) K. R. Symon, Mechanics (Addison-Wesley Publishing, Reading, MA, 2 nd Edition, 1960). 6. ( J ) G. Joos, Theoretical Physics (Hafner Publishing, New York, Third Ed., ca. 1957) 7. ( AS ) A. Sommerfeld, Mechanics (Lectures in Theoretical Physics, Vol. 1; Academic Press, New York, 1952). 8. ( B ) W. E. Byerly, Introduction to the Calculus of Variations (Harvard U. Press, Cambridge, MA, 1928). 9. ( F ) G. R. Fowles and G. L. Cassidy, Analytical Mechanics (Harcourt Brace College/Saunders College, Orlando, FL, 1986). 10. ( K ) E. J. Konopinski, Classical Descriptions of Motion (Freeman, San Francisco, 1969).
PHY 504 Syllabus 4 Fall, 2016 VIII. COURSE SCHEDULE (TENTATIVE; 08/26/14 VERSION) DATE ACTIVITY TOPIC READINGS/HW PART ONE: Review of Newtonian Mechanics W Aug. 24 L1 Historical Background; Generalized G1.1-1.6; L-Introd. Coordinates F Aug. 26 L2 Generalized Coordinates and Constraints G1.3; L1.1-1.4, 1.6 M Aug. 29 L3 Work-Energy Theorem, Conservation of G1.1-1.2; L1.5-1.7 Mechanical Energy HW1 Due PART TWO: Basis of Analytical Mechanics G2.1-2.7 W Aug. 31 L4 Generalized Forces, Classification of G1.3-1.5; L1.6-1.8 Constraints F Sept. 2 L5 Virtual Displacements, Constraints G1.3-1.4, L3.1 HW2 Due M Sept. 5 --- LABOR DAY NO CLASS W Sept. 7 L6 Principle of Virtual Work, Equilibrium G1.4-1.5, L3.1 F Sept. 9 L7 Application of Virtual Work to Rigid G1.2, L3.2-3.3 Body Equilibrium HW3 Due M Sept. 12 L8 d Alembert s Principle: Extension of G1.4-1.6, L4.1-4.3 Principle of Virtual Work to Dynamics W Sept. 14 --- LAST DAY TO DROP COURSE G4.1-4.10 PART THREE: Non-Inertial Systems and Rotations W Sept. 14 L9 Inertial Forces in Accelerating Systems G4.9-4.10, L4.4-4.7 F Sept. 16 L10 Euler Angles and Rigid Body Rotation G4.4, HW4 Due M Sept. 19 L11 Orthogonal Transformations G4.1-4.3 W Sept. 21 L12 Euler s Theorem G4.6 F Sept. 23 L13 Representations of Finite/Infinitesimal Rotations G4.7-4.8, HW5 Due M Sept. 26 L14 Geometry of Rotations; Homework Discussion G4.7-4.8
PHY 504 Syllabus 5 Fall, 2016 DATE ACTIVITY TOPIC READINGS/HW SPECIAL S1 Solving Problems in Noninertial Frames G4.9-4.10, 5.1-5.7; L4.4-4.5 W Sept. 28 L15 Angular Momentum & Rotational Kinetic Energy G5.1 F Sept. 30 L16 Properties of Moment of Inertia Tensor G5.1-5.2; S10.2 HW6 Due M Oct. 3 L17 Principal Axis Transformation G5.3-5.4; S10.3-10.5 W Oct. 5 L18 Symmetry of Inertia Tensor and Steady Motion G5.6; AS4.26; M11.11 PART Four: Hamilton s Principle and Other Advanced Methods F Oct. 7 L19 Intro to Formal Calculus of Variations G2.2; L2.1-2.4, 2.7-2.9; B1-3; HW7 Due M Oct. 10 L20 Derivation of Euler-Lagrange Equations from L2.10-2.12, 2.15 Bernoulli s Principle; Elastic Bar Ex. W Oct. 12 L21 Derivation of Euler-Lagrange Equations from G2.1, 2.3; L5.1-5.2 Hamilton s Principle; Covariance of E-L Eqs. F Oct. 14 HE1 MIDTERM HOUR EXAM G Chapts. 1, 2, 4, 5; L Chapts. 1, 3, 4 SPECIAL S2 Lagrangian Treatment of Symmetrical Top G5.7; M11.9, 11.10 M Oct. 17 --- MIDTERM: TENTATIVE GRADES POSTED G3.1-3.9 M Oct. 17 L22 Hamilton s Principle with Constraints G1.3, 2.4; L2.5, 2.6, 2.12, 3.4-3.5 W Oct. 19 L23 d Alembert s Principle and Constraints G1.4, J5, J6 F Oct. 21 L24 Conservation Theorems for Hamilton s Principle G2.6-2.7; L5.3-5.4; HW8 Due M Oct. 24 L25 Cyclic Coordinates and Routh s Method G2.6-2.7, 8.3; L5.3-5.4 W Oct. 26 L26 Steady Motion S12.6-12.7 F Oct. 28 L27 Central Force Problem: Symmetries, G3.1-3.3; L3.5, 5.2- Effective 1D Potential 5.4; HW9 Due
PHY 504 Syllabus 6 Fall, 2016 DATE ACTIVITY TOPIC READINGS/HW M Oct. 31 L28 Orbit Equation, Virial Theorem, Stability G3.3-3.6 W Nov. 2 L29 The Kepler Problem, Orbital Precession G3.7-3.9 PART FIVE: Principle of Least Action and Hamilton s Equations G8.1-8.6 F Nov. 4 --- LAST DAY TO WITHDRAW FROM COURSE F Nov. 4 L30 Jacobi s Principle, Principle of Least Action G8.6; L5.5-5.7 HW10 Due M Nov. 7 L31 Space Curvature and Geodesics G2.2; L4.8, 5.5-5.7; B T Nov. 8 --- PRESIDENTIAL ELECTION DAY, NO CLASS W Nov. 9 L32 Fermat s Principle, Principle of Least Time G2.2, 8.6 F Nov. 11 L33 Legendre Transforms, Hamilton s Equations G8.1-8.2, 8.5; L6.1-6.4; HW11 Due M Nov. 14 L34 Applications of Hamilton s Equations G8.2; M7.10 W Nov. 16 L35 Canonical Variables and Phase Space G8.1, 8.5; L6.5-6.6 F Nov. 18 L36 Small Oscillations about Static Equilibrium G6.1-6.2; L5.10; HW12 Due M Nov. 21 L37 Principal Axis Transformation, Eigenvectors G6.3; L5.10 Nov. 23-26 --- THANKSGIVING BREAK NO CLASS; G6.1-6.6 M Nov. 28 L38 Orthonormal Eigenvectors (Normal Modes) G6.3; L5.10 W Nov. 30 L39 Forced Oscillations with Damping G6.5 F Dec. 2 L40 Nonlinear Oscillators G6.6; M 4; HW13 Due M Dec. 5 L41 Duffing s Equation; Harmonic Generation M Chapt. 4 W Dec. 7 L42 Duffing s Equation with Damping M Chapt. 4 F Dec. 9 L43 LAST DAY OF CLASS; HW & FINAL EXAM DISCUSSION M Dec. 12 FE FINAL EXAMINATION, CP183, 10:30 to12:30 a.m.
PHY 504 Syllabus 7 Fall, 2016 F Dec. 16 --- SEMESTER ENDS; GRADES DUE TO REGISTRAR