Classical Mechanics 29:5710(old 205)
Classical Mechanics
29:5710
Fall 2018
Class Information
- Room: 618, Van Allen Hall
- Time: 9:30AM - 10:45AM
- Days: Tuesday, Thursday
- Texts:
Mechanics,
L. D. Landau and E. M. Lifshitz,
Lectures on Quantum Mechanics, Paul A. M. Dirac
Lecture Notes.
Instructor Information
- Instructor: Wayne Polyzou
- Office: 306 Van Allen Hall
- Office Hours: Tuesday, Thursday, Friday 10:45-11:30
- e-mail: polyzou@uiowa.edu
- Phone: 319-335-1856
- Grader: TBA
- Grader office: TBA
- Grader phone: TBA
- Grader e-mail: TBA
Grading Policy
Possible final grades are A+,A,B,C,D,F. The grade of A+ is for
performance that is a full grade above an A. Grades are based on
homework scores (20%), mid term exam score (35%), and the final exam
(45%). Homework assignments will appear on the web version of this
syllabus (http://www.physics.uiowa.edu/~wpolyzou/phys205/). Homework
solutions will be posted on links to the electronic syllabus.
The mid-term exam will be given after we complete the discussion of
Lagrangian mechanics.
General Information
My goal is to cover the following topics in roughly the order:
- Newton's laws (Newtonian determinacy, inertial coordinate systems,
inertial mass, non-inertial coordinate systems, gravity)
- Galilean relativity (Galilean group, constraints on interactions,
free particles, special relativity)
- Lagrangian dynamics (virtual work, constraints, generalized coordinates
conservative forces)
- Variational calculus (principle of stationary action,
other applications, second variation)
- Conservation laws and Noether's theorem
- Lagrange multipliers and constraints (forces of constraint,
second variation)
- Oscillators (coupled oscillators, normal modes, driven oscillators,
resonance, parametric oscillations)
- Rigid body motion (fundamental theorem on rigid body motion,
inertia tensor, Euler equations, Euler angles, Cayley Klein parameters (SU(2)),
dynamics, rotating coordinate systems.
- Hamiltonian dynamics (convexity and Legendre transformations,
Hamilton's equations, symplectic eigenvalue theorem, canonical transformations,
Poisson brackets, canonical quantization, symplectic invariants,
scattering, integrable systems, Liouville's theorem,
Poincare recurrence theorem)
- Generalized Hamiltonian dynamics (first and second class constraints,
gauge transformations)
- The classical three body problem,
perturbation theory (Small denominators, KAM theorem)
The material will follow my lecture notes. Most, but not all of
this material appears in the text "Mechanics".
Dirac's book is not really about quantum mechanics. It
is about how to make a Hamiltonian formulation of mechanics when the
Legendre transformation that connects the Lagrangian and Hamiltonian
formulation of mechanics is singular. While this sounds academic, all
of the fundamental forces of nature - the strong, weak, electromagnetic and
gravitational forces (gauge theories) fall into
this class.
Additional References
You may also find the following references useful:
- Classical Mechanics, H. Goldstein (Addison Wesley)
(Standard reference for many years- covers almost everything)
- The Variational Principles of Mechanics, Cornelius Lancoz (Dover)
(Nice book - good historical background - inexpensive)
- Mathematical Methods of Classical Mechanics, V. I. Arnold (Springer Verlag)(The classic reference for modern classical mechanics)
- Theoretical Mechanics of Particles Continua, Fetter and Walecka (Nice presentation - could have more on Hamiltonian dynamics)
The titles below are free to download from a university computer:
Homework Assignments and Calendar
- Week 10 - Out of town this week - classes will be made up
- Tuesday, October 23
-
Lecture 19
-
Homework #9 : due 10/30
- Thursday, October 25 - Out of town this week - classes will be made up
-
Lecture 20
- Final Exam
- December , 618 Van
College Information
Students with Disabilities
Any student who has a disability which may require some
modification of seating, testing, or other class requirements, should
contact me that appropriate arrangements may be made. Students with
disabilities should also contact the Office of Student Disabilities
Services (335-1462).
Student Complaints:
A student who has a complaint related to this course should
follow the procedures summarized below.
Ordinarily, the student should attempt to resolve the matter with
the instructor first. Students may talk first to someone other than
the instructor (the departmental executive officer, or the University
Ombudsperson) if they do not feel, for whatever reason, that they can
directly approach the instructor.
If the complaint is not resolved to the student's satisfaction,
the student should go to the departmental executive officer.
If the matter remains unresolved, the student may submit a written
complaint to the associate dean for academic programs. The associate
dean will attempt to resolve the complaint and, if necessary, may
convene a special committee to recommend appropriate action.
For any complaint that cannot be resolved through the mechanisms
described above, please refer to the College's Student Academic
Handbook for further information.
Additional information: see
teaching policies