Stony Brook University, Department of Physics and Astronomy

 

CLASSICAL MECHANICS
(PHY 501)

Fall 2006

 

A. Initial Information

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

 

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

          J. V. José and E. J. Saletan, Classical Dynamics, Cambridge U. Press, 1998

          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

          H. G. Schuster, Deterministic Chaos, 3rd ed., VCH, Weinheim, 1995



 

B. Syllabus and Course Materials

 (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 Rutherford formula.

 

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; Hamilton equations; Poisson brackets.

          Action. Hamilton’s principle. Hamilton-Jacobi equations.

          Analytical mechanics of continuum as a classical field theory.

          Toward the quantum field theory.