Syllabus

Physics 605: Theoretical Mechanics (Fall 2015)

Class number: 1372(Credit units: 3)

Lecture Room:Adams Room Natural Sciences Building

Lecture Time: 4:00 pm-5:15 pm (Tuesday and Thursday)

Textbook:Classical Mechanics (3rd edition) by Herbert Goldstein, Charles Poole & John Safko (Addison Wesley, 1301 Sansome St., San Francisco, CA, 2002)

Reference books: (1) Classical Mechanics by John Michael Finn (Infinity Science Press LLC, Hingham, Massachusetts, New Delhi, 2008), (2) New Foundations for Classical Mechanics (2nd Edition) by D. Hestenes (Kluwer Academic Publishers, P.O. Box 17, 3300 AA Dordrecht, The Netherlands), (3) Introduction to Dynamics by Ian Percival and Derek Richards (Cambridge, England: Cambridge University Press, NY, 1982)

Instructor: Dr. Ming Yu

Office: Room 242, John W. Shumaker Research Building

Office Hour: 10:00 am – 11:30 am (Monday and Wedensday)

PhoneNumber: 502-852-0931

E-mail:

Web site:

Course Description

Theoretical mechanics deals with the analytical dynamics of systems of particles. The course will introducethe basics concepts (e.g., the generalized coordinates, cyclic coordinates, canonical conjugate momenta, Poisson brackets, Hamilton’s characteristic function, action-angle variables, etc.), the elementary principles including the differential principle (i.e., D’Alembert’s principle) and Variational principle (i.e.., Hamilton’s principle), the Hamiltonian and Lagrangian formulations, and the techniques to work on the equations of motion including canonical transformations, Poisson brackets formulations, and Hamilton-Jacobi formulations which arewidely used in various branches of modern physics (e.g., statistical mechanics, astronomy, wave mechanics,chaos, quantum mechanics, etc.). It will cover the topics the Lagrange equations of motion (Chapter 1), varitional principles (Chapter 2), central force problem (nonrelativistic) (Chapter 3),Hamiltonequationsof motion (Chapter 8), canonical transformations (Chapter 9), Hamilton-Jacobi theory and action-angle variables (Chapter 10). Depending on time available, we might possibly cover the optional topics as listed in the “Topics covered”.

You are encouraged to read the chapters and sections related to these topics from the textbook and reference books and to discuss with your fellow studentsor the instructor to make clear in concepts and in solving assigned problems. Your progress in this area will be assessed with a graded assignment (homework assignment, and embedded in exam questions).

Course Requirements

Mechanics (PHYS 460) and Mathematical Physics (PHYS 561 & PHYS 562)

Goal

The aim of this course is to broaden and deepen our knowledge and to improve critical thinking skills andproblem solving skill in studying various branches of modern physics such as statistical mechanics, astronomy, and quantum mechanics. It is also expected, through this course, for us to master many of the mathematical techniques which are necessary for modern physics.

Topics covered

  1. Differential Principle and Lagrangian Formulations
  2. Mechanics of a systems of particles (Chapter 1.1-2)
  3. Constraints (Chapter 1.3)
  4. D’Alembert’s principles and Lagrange’s equations of motion (Chapter 1.4-6)
  5. Variational Principles and Largrange’s Equations of Motion
  6. Hamilton’s Principle (Chapter 2.1-2)
  7. Lagrange’s equations and Hamilton’s principle (Chapter 2.3-5)
  8. Conservation theorems (Chapter 2.6-7)
  9. Central Force Problem
  10. Equation of motion (Chapter 3.1-2)
  11. Orbits (Chapter 3.3-6)
  12. Kepler problem (Chapter 3.7-9)
  13. Scattering (Chapter 3.10-11)
  14. The Three-body problem (Chapter 3.12)
  15. Hamilton’s Equations of Motion
  16. Lagendre transformation and Hamilton equations of motion (Chapter 8.1)
  17. Cyclic coordinates and conservation theorems (Chapter 8.2)
  18. Derivation of Hamilton’s equations (Chapter 8.5)
  19. The principle of least action (Chapter 8.6-Optional)
  20. Canonical transformations
  21. The equations of canonical transformation (Chapter 9.1-3)
  22. The symplectic approach (Chapter 9.4)
  23. Poisson brackets (Chapter 9.5-7)
  24. Symmetry groups (Chapter 9.8-Optional)
  25. Liouville’s theorem (Chapter 9.9-Optional)
  26. Hamilton-Jacobi Theory and Action-Angle Variables
  27. Hamilton-Jacobi equation (Chapter 10.1-2)
  28. Hamilton’s characteristic function (Chapter 10.3-4)
  29. Ignorable coordinates and Kepler problem (Chapter 10.5)
  30. Action-angle variables (Chapter 10.6-7-Optional)
  31. Kepler problem (Chapter 10.8-Optional)

Homework

Homework assignments for each chapter will be distributed at the middleof each chapter. The corresponding due dates for Homework will be written on the Homework assignments. You are asked to accomplish the general problems. Your solutions for each problem must include not only the final answersbut intermediate steps. Homework assignments will be collected and graded, and form part of your final score. You may discuss homework problems with your fellow students. In fact, you are encouraged to work as a group. However, the final write-up must be your own.

Exams

There will be two in-class exams: one is the midterm exam and the other is the final exam. The midterm exam is tentatively scheduled on Oct. 1-8, and the final exam is scheduled on Dec. 3-10.

Class Participation

Class participation will be monitored throughout the semester. You are basically required to attend the class otherwise, with an excuse.Each absence without an excuse will cost 0.5 point. It is true that certain individuals are able to learn physics solely from a textbook and may think that lectures are unnecessary. It is also true that most part of the course follows the text book basically, but (1) more explanations which do not appear in a typical textbook will be given in class (2) some of the topics of the course are even not covered by the textbook. Participation will provide you the opportunity to gain more, to ask questions as well as clarifying explanations.

Grading Policy

The final scores will be based on the two exams and the homework with breakdown as follows:

Homework 30%

Midterm Exam 35%

Final Exam 35%

The letter grades will be assigned based on the final scores. The approximate cutoffs are:

Grade A+AA_B+BB_C+CC_D+D D-

Cutoff 9690827570655550413835 32

* Please note that the scheduled exam date and above cutoffs are tentative. The instructor reserves the

right to lower the cutoffs if deemed necessary. The cutoffs, however, will not be raised in any cases.

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