Instructor:
Office:
Rm. B-135
Phone:
2-8159
E-mail:
klikharev@notes.cc.sunysb.edu
Office
hours: Thursday 2:00 to 4:00 pm
Grader:
Vladimir
Khachatryan
Office: Rm. C-123
E-mail: vkhachatryan@ic.sunysb.edu
Office hours: Thursday 2:00 to 4:00 pm
Basic textbook:
L. Landau and E.
Lifshitz, Mechanics, 3rd
ed. Butterworth-Heinmann, 1976
Additional reading from:
A. Andronov, A.
Witt, and
A.
L. Fetter and J. D. Walecka, Theoretical
Mechanics of Particles and Continua, McGraw Hill, 1980
H. Goldstein, C. P.
Poole, and J. L. Safko, Classical Mechanics, 3rd ed., Addison
Wesley, 2002
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:
Mon-Wed-Fri 9:35 – 10:30 am, Rm. P-112
Homeworks:
-
weekly (with a few exceptions)
-
late submission policy: minus 10% points a day
Exams (books open):
-
midterm: Friday Oct. 16 (lecture time and room)
- final: Monday Dec. 14 (11:15 am – 1:45 pm, lecture room)
Finite grade components:
-
homeworks: 15%
- midterm exam: 25%
- final exam: 60%
(with approximate lecture count)
1.
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. Simple one-dimensional and
1D-reducible problems (3) Lecture notes
Fixed points
and stability.
General
properties of Hamiltonian 1D systems.
Planetary
motion.
Particle
scattering.
4. 1D
oscillations (7) Lecture notes
Linear (free,
damped, and forced) oscillations.
Weakly nonlinear
oscillations; small parameter method; van der Pol method.
Self-oscillations,
parametric oscillations, and phase locking.
Strongly
nonlinear systems; numerical methods; “curse of dimensionality”.
Harmonic and
subharmonic oscillations.
5. From
oscillations to waves (4) Lecture notes
2 coupled
oscillations; anticrossing diagram. N coupled
oscillators.
1D waves in
periodic systems. Boundary and interface phenomena.
Parametric
and nonlinear effects.
6. Elasticity theory (5) Lecture notes
Deformation,
strain and stress tensors.
Hooke’s law,
elastic moduli.
Equilibrium
condition; beam bending; rod torsion.
Elastic
waves.
7. Rigid body motion (6) Lecture notes
Rotation;
inertia tensor; kinetic energy and angular momentum.
Fixed-axis
case; rotation coupled with translation.
Dynamics of
tops; torque-induced precession, Euler angles.
Kinematics
and dynamics in non-inertial reference frames.
8. Fluid dynamics (4) Lecture notes (only 2 first
sections so far)
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.
9. Chaos (2)
Chaos in
maps, logistic map.
Chaos in
dynamic systems; the Lorentz system and forced nonlinear oscillator.
Chaos in
Hamiltonian systems; the Hénon-Heiles system; integrable and mixing billiards.
Quantum
mechanics of classically chaotic systems; level repulsion.
Chaos vs. turbulence.
10. Hamiltonian and
Hamilton-Jacobi formalisms (3)
Generalized
momentum;
Action.
Analytical
mechanics of continuum as a classical field theory.
Toward the
quantum field theory (time permitting).
Optional problems
Set 1 with solutions
Optional problems
Set 2 with solutions
Homework 8 (due Friday
Nov. 20)
Homework 9 (due
Monday Nov. 30)
Post-Thanksgiving
milestones:
Monday Nov.
30: Homework 9 due; Homework 10
assigned
Friday Dec.
4: Set 3 of optional problems
distributed
Monday Dec.
7: Homework 10 due
Wednesday
Dec. 9: Model solutions of all homeworks and optional Set 3 distributed
Thursday Dec.
10: Review session (time TBD)
Monday Dec.
14: Final exam
Americans with
Disabilities Act: