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)
Phone Number: 502-852-0931
E-mail: m0yu0001@louisville.edu
Web site: http://www.physics.louisville.edu/yu/
Course Description
Theoretical mechanics deals with the analytical dynamics of systems of particles. The
course will introduce the 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 are widely 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), Hamilton equations of 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 students or 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 and problem 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
1.1 Mechanics of a systems of particles (Chapter 1.1-2)
1.2 Constraints (Chapter 1.3)
1.3 D’Alembert’s principles and Lagrange’s equations of motion (Chapter
1.4-6)
2. Variational Principles and Largrange’s Equations of Motion
2.1 Hamilton’s Principle (Chapter 2.1-2)
2.2 Lagrange’s equations and Hamilton’s principle (Chapter 2.3-5)
2.3 Conservation theorems (Chapter 2.6-7)
3. Central Force Problem
3.1 Equation of motion (Chapter 3.1-2)
3.2 Orbits (Chapter 3.3-6)
3.3 Kepler problem (Chapter 3.7-9)
3.4 Scattering (Chapter 3.10-11)
3.5 The Three-body problem (Chapter 3.12)
4. Hamilton’s Equations of Motion
4.1 Lagendre transformation and Hamilton equations of motion (Chapter 8.1)
4.2 Cyclic coordinates and conservation theorems (Chapter 8.2)
4.3 Derivation of Hamilton’s equations (Chapter 8.5)
4.4 The principle of least action (Chapter 8.6-Optional)
5. Canonical transformations
5.1 The equations of canonical transformation (Chapter 9.1-3)
5.2 The symplectic approach (Chapter 9.4)
5.3 Poisson brackets (Chapter 9.5-7)
5.4 Symmetry groups (Chapter 9.8-Optional)
5.5 Liouville’s theorem (Chapter 9.9-Optional)
6. Hamilton-Jacobi Theory and Action-Angle Variables
6.1 Hamilton-Jacobi equation (Chapter 10.1-2)
6.2 Hamilton’s characteristic function (Chapter 10.3-4)
6.3 Ignorable coordinates and Kepler problem (Chapter 10.5)
6.4 Action-angle variables (Chapter 10.6-7-Optional)
6.5 Kepler problem (Chapter 10.8-Optional)
Homework
Homework assignments for each chapter will be distributed at the middle of 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 answers but 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+
A
A_
B+
B
B_
C+
C
C_
D+
D
D-
Cutoff 96
90
82
75
70
65
55
50
41
38
35
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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