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Ejs Liouville’s Theorem Phase Space Plotter Model
written by Juan Aguirregabiria
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).
1 source code document is available
Subjects Levels Resource Types
Oscillations & Waves
- Oscillations
= Damped Oscillators
= Pendula
= Simple Harmonic Motion
- Upper Undergraduate
- Instructional Material
= Activity
= Interactive Simulation
Intended Users Formats Ratings
- Learners
- Professional/Practitioners
- Educators
- application/java
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Access Rights:
Free access
Restriction:
© 2008 Juan M. Aguirregabiria
Additional information is available.
Keywords:
Easy java Simulations, Ejs, Liouville, Liouville's theorem, OSP, Open Source Physics, pendulum, phase space, simple harmonic motion
Record Creator:
Metadata instance created July 10, 2008 by Mario Belloni
Record Updated:
June 5, 2014 by Andreu Glasmann
Last Update
when Cataloged:
July 1, 2008
ComPADRE is beta testing Citation Styles!

Record Link
AIP Format
J. Aguirregabiria, Computer Program EJS LIOUVILLE’S THEOREM PHASE SPACE PLOTTER MODEL, Version 1.0 (2008), WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=7606&DocID=605).
AJP/PRST-PER
J. Aguirregabiria, Computer Program EJS LIOUVILLE’S THEOREM PHASE SPACE PLOTTER MODEL, Version 1.0 (2008), <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=7606&DocID=605>.
APA Format
Aguirregabiria, J. (2008). Ejs Liouville’s Theorem Phase Space Plotter Model (Version 1.0) [Computer software]. Retrieved October 3, 2024, from https://www.compadre.org/Repository/document/ServeFile.cfm?ID=7606&DocID=605
Chicago Format
Aguirregabiria, Juan. "Ejs Liouville’s Theorem Phase Space Plotter Model." Version 1.0. https://www.compadre.org/Repository/document/ServeFile.cfm?ID=7606&DocID=605 (accessed 3 October 2024).
MLA Format
Aguirregabiria, Juan. Ejs Liouville’s Theorem Phase Space Plotter Model. Vers. 1.0. Computer software. 2008. Java (JRE) 1.5. 3 Oct. 2024 <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=7606&DocID=605>.
BibTeX Export Format
@misc{ Author = "Juan Aguirregabiria", Title = {Ejs Liouville’s Theorem Phase Space Plotter Model}, Month = {July}, Year = {2008} }
Refer Export Format

%A Juan Aguirregabiria %T Ejs Liouville's Theorem Phase Space Plotter Model %D July 1, 2008 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=7606&DocID=605 %O 1.0 %O application/java

EndNote Export Format

%0 Computer Program %A Aguirregabiria, Juan %D July 1, 2008 %T Ejs Liouville's Theorem Phase Space Plotter Model %7 1.0 %8 July 1, 2008 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=7606&DocID=605


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The AIP Style presented is based on information from the AIP Style Manual.

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