Instructor: Prof.
Konstantin Likharev
Phone:
2-8159
E-mail:
klikharev@notes.cc.sunysb.edu
Office
hours: Thursday 4:30 to 6:30 pm, Rm. B-135
Web site: http://rsfq1.physics.sunysb.edu/~likharev/501/F04/index.html
Basic Textbook:
L. Landau and E. Lifshitz, Mechanics,
3rd ed. Butterworth-Heinmann, Oxford, 1976
Additional Reading
From:
A. Andronov, A. Witt, and S. Khaikin, Theory
of Oscillators, Pergamon, 1966
L. Landau and E. Lifshitz, Theory
of Elasticity, 3rd ed. Butterworth-Heinmann, Oxford, 1986
L. Landau and E. Lifshitz, Fluid
Mechanics, 2nd ed. Butterworth-Heinmann, Oxford, 1987
J. José and E. Saletan, Classical
Dynamics: A Contemporary Approach, Cambridge U. Press, 1998
Lectures: Approximately 40 lectures,
Mon-Wed-Fri 9:35-10:30 am, Rm. P-112
Homeworks: Weekly (with just a few exceptions)
Exams: Two midterms and a final exam
All exams: books open
Grade
Components:
Homeworks:
20%
Midterms:
30%
Final
exam: 50%
(with approximate
lecture count):
1. Introduction and review of
fundamentals (2)
Kinetics;
dynamics; momentum; energy and work; angular momentum; many-particle systems.
2. Lagrangian formalism (3)
Constrains and
generalized coordinates; Lagrange equations.
Hamiltonian and
energy conservation.
3. 1D motion (8)
General properties
of Hamiltonian systems.
Linear (free,
damped, and forced) oscillations.
Strongly nonlinear
systems; numerical methods.
Weakly nonlinear
and parametric oscillations; small parameter analysis; Van der Pol method.
4. 2D motion (5)
Coupled
oscillations.
Central force
motion; Kepler laws.
Collisions and
scattering; the Rutherford formula.
5. Rigid body motion (5)
Rotation; inertia
tensor; kinetic energy and angular momentum.
Spinning tops.
Translation plus rotation.
Dynamics in
non-inertial reference frames.
6. Elasticity theory (5)
Elasticity theory
fundamentals; bending beams; torsion rods.
Elastic dynamics;
acoustic waves.
Lagrangian
formalism for continuum dynamics.
7. Fluid dynamics (5)
Fluid statics and
dynamics; Euler and Navier-Stokes equations.
Turbulence; the
Reynolds number.
Shock waves; the
Mach number.
8. Chaos (3)
Chaos in maps,
logistic map.
Chaos in dynamic
systems; forced pendulum.
Chaos in
Hamiltonian systems; the Henon map.
Chaos vs.
turbulence.
9. Hamiltonian and Hamilton-Jacobi formalisms (3)
Hamilton principle.
Generalized
momentum; Hamilton equations; Poisson brackets.
Hamilton-Jacobi
equations.