7. Dissipation, Driving, and Chaos -- the Driven Pendulum

• The nonlinear pendulum
  • derivation of the equations of motion
  • integration using the predictor-corrector scheme

• C++ and Python programs as starting points

• Damped motion
  • form of the damping term
  • integration of the motion
  • in-class exercise 7.1
  • critical damping

• Damped, driven motion
  • form of the driving term
  • integration of the motion
  • phase space plots
  • transients and periodic motion
  • in-class exercise 7.2
  • choice of parameters -- periodic and chaotic motion

• Visualizing chaotic motion -- Poincaré sections

• Homework #5