A Chaotic Pendulum in Phase Space with Java

Contents of Applets

• Complicated behavior
  • shows a moving pendulum
  • pendulum bob turns white when moving fast
  • simultaneously plots angular position vs time (dynamic scaling of axis)
  • simultaneously plots trajectory in phase space (dynamic scaling)
  • optionally displays power spectrum (square of Fourier components); run for long time to be realistic
  • tabulated standard cases
• Comparison of two chaotic pendula
  • shows two moving pendula
  • see how sensitivity to initial conditions develops
  • eventually motion always looks different
  • pendulum bob turns white when moving fast
  • tabulated standard cases
  • simultaneously plots trajectories in phase space (dynamic scaling)

• Equation of Motion
• What are Pendulum Applets?
• Running Our Two Applets
• Suggested Explorations

Applets by Hans Kowallik of the Landau Research Group
Oregon State University, Corvallis, Oregon