Physics 501
Classical Mechanics
Fall 2011
Monday, Wednesday, Friday, 9:35am-10:30am.
Physics P-112
Graded homework 10 is available just outside of my office B-102.
Instructor: Sasha Abanov,
Associate Professor
Office: Physics B102
Phone: (631)632-8174
E-mail: alexandre.abanovatsunysb.edu
Web page:
http://felix.physics.sunysb.edu/~abanov/
Office Hours:
Wed 10:30-11:30am
Teaching Assistant: Li Yan
Office: Physics C-119
E-mail: li.yanatstonybrook.edu
Course description
Lagrangian and Hamiltonian formulations with applications to various dynamical systems. Variational principles, symmetries and conservation laws. Hamilton-Jacobi theory. Introduction to selected advanced subjects such as nonlinear oscillations, parametric oscillations, classical perturbation theory, integrable and chaotic systems, theory of elastic field.
Course requirements
Attendance to lectures is expected. Homework assignments should be turned in on time. Late homeworks will not be accepted. There will be two midterms and a final exam.
Grading and exams
Two midterms (September 26 and November 16) and a final exam (December 19) All exams: book open.
The final grade is calculated from
| Homeworks |
--- |
20% |
| Midterms |
--- |
20+20% |
| Final exam |
--- |
40% |
Tentative Syllabus of the Course (Schedule)
- Introduction.
- Lagrangian formalism.
- Conservation laws.
- 1D motion.
- 2D motion. Central force motion.
- Small oscillations.
- Rigid body motion.
- Hamiltonian and Hamilton-Jacobi formalism.
- Nonlinear dynamics and chaos.
- Elasticity theory.
- Dynamics of continuous systems.
- Final remarks: towards field theory and quantum mechanics.
Homeworks
-
Homework #1, due Monday, September 12
(PDF )
Variational calculus/principle
-
Homework #2, due Monday, September 19
(PDF )
Conservation laws
-
Homework #3, due Monday, September 26
(PDF )
1D Motion. Central force problem in 2D.
-
Homework #4, due Wednesday, October 5
(PDF )
Central force problem. Scattering.
-
Homework #5, due Friday, October 14
(PDF )
Scattering. Small oscillations.
-
Homework #6, due Friday, October 21
(PDF )
Small oscillations. Rotations. Inertia tensor.
-
Homework #7, due Friday, October 28
(PDF )
Rigid body motion. Coriolis force.
-
Homework #8, due Friday, November 4
(PDF )
Poisson's brackets. Canonic transformations.
-
Homework #9, due Monday, November 14
(PDF )
Hamilton-Jacobi equation. Action-angle variables. Adiabatic invariants.
-
Homework #10, due Monday, December 5
(PDF )
Perturbation theory. Logistic equation. Parametric resonance.
-
Homework #11, Not for credit
(PDF )
Mechanics of continuous media.
Textbooks
Main textbook
-
L. Landau and E. Lifshitz, v. 1: Mechanics,
Butterworth-Heinemann, Oxford, Third edition, 1976.
-
H. Goldstein, C.P. Poole, J.L. Safko, Classical Mechanics,
Addison-Wesley, Oxford, Third edition, 2002.
For additional reading I also recommend
-
A. L. Fetter and J. D. Walecka,
Theoretical Mechanics of Particles and Continua,
Dover Publications, 2003.
-
L. Landau and E. Lifshitz, v. 6: Fluid Mechanics,
Butterworth-Heinemann, Oxford, Second edition, 1987.
-
L. Landau and E. Lifshitz, v. 7: Theory of Elasticity,
Butterworth-Heinemann, Oxford, Third edition, 1986.
-
G. Falkovich, Fluid Mechanics: A Short Course for Physicists,
Cambridge University Press, 2011.
-
J. Jose and E. Saletan, Classical Dynamics: A Contemporary Approach,
Cambridge University Press, 1998.
-
V. I. Arnold, A. Weinstein and K. Vogtmann,
Mathematical Methods of Classical Mechanics (Graduate Texts in Mathematics), 2nd edition, Springer, 1989.
For your information.
If you have a physical, psychological, medical or learning disability that
may impact your course work, please contact Disability Support Services
(631) 632-6748. They will determine with you what accommodations are
necessary and appropriate. All information and documentation is
confidential.
Students requiring emergency evacuation are encouraged to discuss their
needs with their professors and Disability Support Services. For
procedures and information, go to the following web site
http://studentaffairs.stonybrook.edu/dss/
Last updated December 5, 2011