Particle in a Standing Wave Field

This Demonstration shows the phase portrait of the Hamilton equations that describe the motion of a particle of mass and charge in the field of a standing wave. You can see separatrices corresponding to resonance with waves.

SNAPSHOTS

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

DETAILS

The equation of motion is
.
Choosing and defining gives a time-dependent Hamiltonian
.
Reference
[1] J. Candy and R. Rozmus, "A Symplectic Integration Algorithm for Separable Hamiltonian Functions," Journal of Computational Physics, 92(1), 1991 pp. 230–256. doi:10.1016/0021-9991(91)90299-Z.
    • 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.