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. |
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).