MECHANICS, Phys 505

Fall 1998

Instructor: Aurel Bulgac

Office: PAB B478
Phone: 685-2988
E-mail: bulgac@phys.washington.edu
Office hours: by appointment or just drop in, but better call or better still e-mail me before.

Teaching Assistant: Mee-soon Ha

Office: PAB B426
Phone: 543-5074
E-mail: msha@phys.washington.edu


Grading algorithm: 30% homework + 30% midterm + 40% final exam

Midterm exam: Monday, November 2-nd
Final exam: Tuesday, December 15, 2:30 - 4:20 pm

Exams are closed book.

HOMEWORK ASSIGNMENTS

Homework is due a week after it is assigned.
Homework is to be done individually, not collaboratively.
You might be able to find solutions by asking around or by some other means,
I strongly suggest that you do not attempt that, but instead try to work them out by yourself.
Late homework will not be accepted,  as a rule.

The first person to find a nontrivial mistake in the solutions will get extra credit.

Solutions will be posted here. When they become available, the corresponding problem numbers will appear as links.
Note, each page is displayed as a separate link.

Index


COMPUTER PROJECTS
  • Foucault pendulum , text file with short explanation on how to use matlab to visualize the trajectory of a Foucault pendulum. The following matlab file foucault.m should be downloaded to your disk and named exactly the same way.

  • Trajectory in a gravitational potential. The following matlab files satellite.m and trajectory.m are to be downloaded to your disk space and named exactly as they are here.

  • Satellite.m - Trajectory.m These are two more, somewhat simplified variants of the files above above.

  • The following matlab files sat.m and traj.m are to be downloaded to your disk space and named exactly as they are here. Thus, when calling them, replace the command at the prompt satellite(...) with sat(...) in the previous example. These files contain a very small change when compared to the previous example. In the potential energy -GMm/r I have replaced r=sqrt(x^2+y^2+z^2) with r=sqrt(a^2x^2+y^2+z^2) where a=1.03. The potential is not central anymore and the bound trajectories are not closed as in the case of the 1/r potential.
    In this case you can generate genuine 3d-trajectories. Experiment with various initial conditions and for ploting use instead of plot(x,y) the 3d-function plot3(x,y,z). Issue after that the commands xlabel('X'),ylabel('Y'),zlabel('Z'), grid on, rotate3d on and after that rotate the figure with the mouse while holding down the right button.

  • November 4 . Three matlab files NonOsc.m, Force.m, Amplitude.m, and some explanations explanations and two figures NonOsc.ps, Amplitude.ps.

    Here are Three files Check.m, NonS.m, ForS.m, which solve the homework problem. Download them in matlab issue the command Check .
     
  • Fermi-Pasta-Ulam problem
     
  • Lorenz model , Lorenz.m, XYZdot.m .
     
  • The following three matlab files PSS.m , Poin.m, PXVdot.m generate the phase space portrait (the red circles are the points used in the Poincare plot), the Poincare surface of section (stroboscopic pictures of the phase space portrait at time = n*Tdrive) and the time series for the angle and angular velocity for the physical driven pendulum with damping. The relevant parameters are defined in the file PSS.m. After downloading these files to your directory, at the matlab prompt type PSS and the three part plot will be generated. The first 50 periods are skipped and the remaining 30 are used to generate the plots. In all three plots you can zoom in and out with the mouse. For better viewing stretch the plot window in the vertical direction.

    Tomorrow (Thursday, November 19) I shall put on reserve in the Physics library two books: Alejandro L. Garcia, Numerical Methods for Physics (which teaches numerical methods and matlab, with programs in matlab and fortran, available on line ) and Gregory L. Baker and Jerry P. Gollub, Chaotic Dynamics: an introduction (the name says it all, I have used today, Wednesday, November 18, some pictures from it). If you cannot quite reproduce some pictures from the book, and if you are extremely and very confident in your program, the reason might be that the numbers quoted in the text are not accurate enough.
     
Index

Textbook:  Theoretical Mechanics of Particles  and Continua, Alexander L. Fetter and John Dirk Walecka.

Tentative syllabus

1.  Review

2.  Lagrangian Dynamics
          * constrained motion
          * calculus of variations
          * Lagrange's equations

3.  Small Oscillations and Normal Modes
          * two coupled oscillators
          * N-body problems

4.  Coupled Oscillators and Related Quantum Mechanics Problems
          * time dependent moments: level crossings
          * matter-enhanced neutrino oscillations
            and the Landau-Zener approximation
 
5.  Anharmonic Oscillations
          * Quadratic and cubic restoring forces
          * Numerical methods

6.  Hamiltonian Dynamics
          * Hamiltonian-Jacobi Equation
          * Connection to Quantum Mechanics
          * Poisson Brackets

7.  Chaotic Systems
           * Damped, Driven Oscillator
           * Chaotic and Regular Trajectories
           * Attractors
           * Phase Space and the Poincare Plot

8.  Strings and Membranes
           (Chapt. 8: only if we go faster than expected) 
Index