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 problems (9) Lecture Notes
(almost complete)
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.
Subharmonic
oscillations.
4. 2D motion problems (5) Lecture Notes (first part only)
Coupled
oscillations; anticrossing diagram.
Central force
motion; effective mass; Kepler laws.
Scattering;
the
5. Rigid body motion (5)
Rotation;
inertia tensor; kinetic energy and angular momentum.
Symmetric
tops; Euler angles.
Translation
plus rotation.
Kinematics
and dynamics in non-inertial reference frames.
6. Elasticity theory (5)
Deformation,
strain and stress tensors.
Hooke’s law,
elastic moduli.
Equilibrium
condition; beam bending; rod torsion.
Elastic
dynamics; acoustic waves.
7. Fluid dynamics (5)
Fluid statics
and dynamics.
Euler and
Navier-Stokes equations, analytical and numerical methods of their solution.
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 Hénon-Heiles system; integrable and mixing billiards.
Quantum
mechanics of classically chaotic systems; level repulsion.
Chaos vs.
turbulence.
9. Hamiltonian and
Hamilton-Jacobi formalisms (4)
Generalized
momentum;
Analytical
mechanics of continuum as a classical field theory.
A route to
the quantum field theory.