Monday, Wednesday, Friday, 9:35am-10:30am.
Graded homework 10 is available just outside of my office B-102.
Instructor: Sasha Abanov,
Office: Physics B102
Teaching Assistant: Li Yan
Office: Physics C-119
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.
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
Tentative Syllabus of the Course (Schedule)
- 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.
Homework #1, due Monday, September 12
Homework #2, due Monday, September 19
Homework #3, due Monday, September 26
1D Motion. Central force problem in 2D.
Homework #4, due Wednesday, October 5
Central force problem. Scattering.
Homework #5, due Friday, October 14
Scattering. Small oscillations.
Homework #6, due Friday, October 21
Small oscillations. Rotations. Inertia tensor.
Homework #7, due Friday, October 28
Rigid body motion. Coriolis force.
Homework #8, due Friday, November 4
Poisson's brackets. Canonic transformations.
Homework #9, due Monday, November 14
Hamilton-Jacobi equation. Action-angle variables. Adiabatic invariants.
Homework #10, due Monday, December 5
Perturbation theory. Logistic equation. Parametric resonance.
Homework #11, Not for credit
Mechanics of continuous media.
For additional reading I also recommend
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.
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
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
Last updated December 5, 2011