Instructor: Konstantin
Likharev
Office:
B-135
Phone:
2-8159
E-mail: klikharev@notes.cc.sunysb.edu
Office hours:
Thursday 3:00 to 4:30 pm
Grader:
Constantinos Constantino
Office: C-118
Phone: 2-4076
E-mail: constant@grad.physics.sunysb.edu
Office hours: Monday and Friday 3:00
to 4:00 pm
Web site: http://rsfq1.physics.sunysb.edu/~likharev/501/F06/
Basic Textbook:
L. Landau and E.
Lifshitz, Mechanics, 3rd ed. Butterworth-Heinmann,
Additional
A. Andronov, A.
Witt, and
H.
Goldstein, Classical Mechanics, 2nd ed., Addison Wesley, 1980
J.
V. José and E. J. Saletan, Classical
Dynamics,
L. Landau and E.
Lifshitz, Theory of Elasticity, 3rd
ed., Butterworth-Heinmann,
L. Landau and E.
Lifshitz, Fluid Mechanics, 2nd
ed., Butterworth-Heinmann,
H. G. Schuster, Deterministic Chaos, 3rd ed., VCH, Weinheim, 1995
Lectures: 41 lectures, Mon-Wed-Fri 9:35-10:30 am,
Rm. P-112
Homeworks: Weekly (with just one or two exceptions)
Exams: Two midterms (October 16 and November 20) and a final (December
20)
All exams: books open
Grade
Components:
Homeworks:
30%
Midterms:
15%+15%
Final
exam: 40%
(with approximate lecture count)
1.
Introduction and review of fundamentals (2) Lecture Notes
Kinematics; dynamics; momentum; Newton
Laws.
Angular momentum; work and energy.
2. Lagrangian formalism (3) Lecture
Notes
Constrains
and generalized coordinates.
Generalized
forces, Lagrange equations.
Generalized
momentum; Hamiltonian and energy conservation.
3. 1D motion (9) Lecture Notes
Fixed points
and stability.
General
properties of Hamiltonian systems.
Linear (free,
damped, and forced) oscillations.
Weakly
nonlinear oscillations; small parameter method.
Van der Pol
method, self-oscillations; parametric oscillations.
Strongly
nonlinear systems; numerical methods.
Harmonic and
subharmonic oscillations.
4. Some problems of 2D motion (5) Lecture Notes
Coupled
oscillations; anticrossing diagram; parametric coupling.
Central force
motion; effective mass; Kepler laws.
Scattering;
the
5. Rigid body motion (6) Lecture Notes
Rotation;
inertia tensor; kinetic energy and angular momentum.
Dynamics of spherical
and symmetric tops; Euler angles.
Rotation
coupled with translation.
Kinematics
and dynamics in non-inertial reference frames.
6. Elasticity theory (6) Lecture Notes
Deformation,
strain and stress tensors.
Hooke’s law,
elastic moduli.
Equilibrium
condition; beam bending; rod torsion.
Elastic
dynamics; acoustic waves.
7. Fluid dynamics (4) Lecture Notes
Fluid statics
and kinematics.
Euler
equation; ideal fluid flow.
Viscosity,
Navier-Stokes equation.
Analytical
and numerical methods in viscous fluid problems.
The Reynolds
number, turbulence.
8. Chaos (2) Lecture Notes (to be concluded)
Chaos in
maps, logistic map.
Chaos in
dynamic systems; forced pendulum.
Chaos in
Hamiltonian systems; the Hénon-Heiles system; integrable and mixing billiards.
Quantum
mechanics of classically chaotic systems; level repulsion.
Chaos vs.
turbulence.
9. Hamiltonian and
Hamilton-Jacobi formalisms (3) Lecture Notes (to be
completed)
Generalized
momentum;
Action.
Analytical
mechanics of continuum as a classical field theory.
A route toward
the quantum field theory.