Stony Brook University, Department of Physics and Astronomy

 

CLASSICAL MECHANICS AND DYNAMICS
(PHY 501)

Fall 2009

 

A. Initial Information

Instructor:  

            Konstantin Likharev

          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 S. Khaikin, Theory of Oscillators, Pergamon, 1966

     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, 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

 

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%

 

B. Syllabus

 (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; Hamilton equations; Poisson brackets.

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

         

 

C. Course Materials

Selected mathematical formulas

Selected physical constants

 

Optional problems Set 1 with solutions

Optional problems Set 2 with solutions

Optional problems Set 3 with solutions

 

Homework 1 with solutions

Homework 2 with solutions

Homework 3 with solutions

Homework 4 with solutions

Homework 5 with solutions

Homework 6 with solutions

Homework 7 with solutions

Homework 8 with solutions

Homework 9 with solutions

Homework 10 with solutions

 

Midterm exam with solutions

Final exam with solutions

 

 

D. University-Mandated Statements

Americans with Disabilities Act: If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disability Support Services, ECC (Educational Communications Center) Building, room128, (631) 632-6748. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential.

 Academic Integrity: Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty are required to report and suspected instances of academic dishonesty to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website at http://www.stonybrook.edu/uaa/academicjudiciary/ .

 Critical Incident Management: Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn.