Chaotic Motion of Perturbed Pendulum

From the Hamiltonian corresponding to a pendulum with a rotating point of suspension, this Demonstration calculates the phase portrait showing chaotic dynamics, whose most notable feature is the existence of a separatrix.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

The Hamiltonian is
,
where is the frequency of small oscillations for the unperturbed case, is a dimensionless parameter of perturbation chosen to be small, and is the frequency.
Reference
[1] G. M. Zaslavsky, Physics of Chaos in Hamiltonian Systems, 2nd ed., London: Imperial College Press, 2007 pp. 14–17.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.