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 Lecture notes
Kinematics; dynamics; momentum; Newton
Laws.
Angular momentum; work and energy.
2. Lagrangian formalism Lecture notes
Constrains
and generalized coordinates.
Generalized
forces, Lagrange equations.
Generalized
momentum; Hamiltonian and energy conservation.
3. 1D problems Lecture
notes
Fixed points
and stability.
General
properties of Hamiltonian 1D systems.
Planetary
motion.
Particle scattering.
4. Oscillations
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 Lecture notes
2 coupled
oscillations; anticrossing diagram. N coupled
oscillators.
1D waves in periodic
systems. Boundary and interface phenomena.
Parametric
and nonlinear effects.
6. Rigid body motion 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.
7. Deformations and elasticity Lecture notes
Deformation, strain and stress tensors.
Hooke’s law,
elastic moduli.
Equilibrium condition;
beam bending; rod torsion.
Elastic
waves.
8. Fluid dynamics 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.
9. Deterministic chaos Lecture notes
Chaos in maps, logistic map.
Chaos in
dynamic systems; the Lorentz system and forced nonlinear oscillator.
Chaos in Hamiltonian systems.
Chaos vs. turbulence.
10. A bit more
of analytical mechanics Lecture notes
Generalized momentum;
Action.
Selected
mathematical formulas
Optional problems
Set 1 with solutions
Optional problems
Set 2 with solutions
Optional problems
Set 3 with solutions
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