Exploratorium
Lab Works in Applied ODEs

The full list of over 100 examples in various fields pre-loaded in this software may be found in the list of Samples (especially numerous in Celestial Mechanics). There, however, it is explained only what those samples demonstrate, yet no didactical material is offered.

On the contrary, this section is intended as a series of lectures on various topics of applied ODEs (and pure mathematics) illustrated with the dynamic simulation of the respective motion. As of this moment (October 2022) this project is only in an initial stage.

You have to download and install the software of the Taylor Center as explained here. This software runs the library of examples of various physical processes as real time animation in 2D or 3D stereo for viewing via a pair of Red/Blue glasses. (3D stereo appears on black background). If you do not have Red/Blue glasses, you may watch it in conventional axonometry (clicking the respective button).

In order to learn and experiment with the simulations and real time animation here, choose and click at the desired title in the list below. This will lead you to downloading a zipped file. Unzip and place it anywhere preserving the structure. It consists of a pdf file with a lecture and explanations what to do and to expect, and several folders with the script files for the software. While reading the pdf, when you decide to experiment with a particular script file mentioned there, run the software and under File/Open Script navigate to the desired script file (or follow the methods of automation mentioned in the Appendix of the pdf files). Then Play it putting the glasses on.

Mechanics

The Rigid Body

The Guide and didactic manual

The simulations
Video clip of the Dzhanibekov effect  covered in the Guide above

Celestial Mechanics

1) Three body free fall periodic orbits: new remarkable features
The same text in pdf

(the article and the links to the supporting simulations)

Dropping bodies – by Richard Montgomery (pdf)

2) A remarkable mapping into the shape space (w₁, w₂, w₃) and shape sphere (u₁, u₂, u₃) for the 3-body problem
The Guide and didactic manual
The simulations

Pure Mathematics

Powers which commute or associates as solutions of ODEs

(the article and the links in the end to the supporting simulations)

Look for a systematized list of other examples in Samples  (meanwhile without didactical explanations).