The Ejs Liouville's Theorem Phase Space Plotter model displays the dynamics of an ensemble of pendula or simple harmonic oscillators in phase space (velocity versus position).  Friction is initially set to zero but can be changed via a textbox as can the number of elements in the ensemble.  The initial starting point of each element in the ensemble forms a particular shape (square, hollow square, disk, or circle).  Therefore at the beginning of the simulation, each starting point is near the others and the red center point in phase space.  For the pendulum ensemble, the Cylinder checkbox keeps the angular position between –pi and pi for large initial angular velocities.  You can modify this simulation if you have Ejs installed by right-clicking within the plot and selecting "Open Ejs Model" from the pop-up menu item.  

Ejs Liouville's Theorem Phase Space Plotter model was created using the Easy Java Simulations (Ejs) modeling tool.  It is distributed as a ready-to-run (compiled) Java archive.  Double clicking the ejs_ehu_analytical_mechanics_Liouville.jar file will run the program if Java is installed.  Ejs is a part of the Open Source Physics Project and is designed to make it easier to access, modify, and generate computer models.  Additional Ejs models for Newtonian mechanics are available.  They can be found by searching ComPADRE for Open Source Physics, OSP, or Ejs.

Please note that this resource requires at least version 1.5 of Java (JRE).