Instructor: Konstantin
Likharev
Phone:
2-8159
E-mail:
klikharev@notes.cc.sunysb.edu
Office
hours: Thursday 4:30 to 6:30 pm, Rm. B-135
Grader:
Miguel Bandres
E-mail:
bandres@gmail.com
Office
hours: Monday and Wednesday 2:00 to 3:00 pm, Rm. C-123
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
H.
Goldstein, Classical Mechanics, 2nd ed., Addison Wesley, 1980
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 (October 4 and November 8) and a final exam (December
15)
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
Generalized
forces, Lagrange equations.
Generalized
momentum; 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 oscillations; small parameter analysis.
Parametric
oscillations, van der Pol method.
Subharmonic
oscillations.
4. 2D motion (5)
Coupled
oscillations; anticrossing diagram.
Central force
motion; effective mass; Kepler laws.
Scattering;
the Rutherford formula.
5. Rigid body motion (5)
Rotation;
inertia tensor; kinetic energy and angular momentum.
Symmetric
tops; Euler angles.
Translation
plus rotation.
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 (4)
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 (3)
Generalized
momentum;
Hamilton
principle. Hamilton-Jacobi equations.
Analytical
mechanics of continuum as a classical field theory.
Toward the
quantum field theory.