29::196 Computational Physics: Assignments  for week 5




Individual projects in Classical  Mechanics. It should have at least three variables and be solvable or integrable in some limit but not in general. Examples that will be discussed
in class (and cannot be used as a project):

• The double pendulum. It has four variables (two angles and two angular velocity) and is integrable if we neglect gravity which is approximately realizes when the total energy is large.  The onset of chaos when the energy is decreased, and subsequently the return to order at low energy can be probed 
  with Poincare sections. A good understanding of RGB and CMYK can be useful: see examples.

•  Matthieu equation. The third dimension is time. Instabilities, parametric resonances can be observed
  in return map for the linear and nonlinear equation.