Phase Plane Plots

This demonstration illustrates a simple phase plane plot. The particular system plotted in this example is

  1. x'=y
  2. y'=1-x+3*x^2/16
It arises when Newton's Law of gravitation is modified to incorporate small corrections due to general relativity. This is needed to explain the precession of the perihelion of Mercury. In this application, the variable x is really one over the usual polar coordinate r and t is really the usual polar coordinate theta.

To plot the trajectory that starts at any specific point, just click the mouse there. The programme stops plotting a trajectory when it reaches the edge of the screen or when the user clicks the "Stop" button. The user may clear the screen by clicking the "Clear" button. By default, trajectories are plotted forwards in time. The user may also chose to have trajectories plotted backwards in time. Just click the "Forwards" button. It toggles between "Forwards" and "Backwards".

The demonstration below is an applet. Google Chrome, Firefox and Microsoft Edge no longer execute applets because of security issues with NPAPI plugins. Some browsers that still play applets are Internet Explorer, Safari and the Pale Moon browser [ windows, linux, Mac ].