Hello,
Since the recent "rk" thread went on a bit, I played with some of the tools
available, and I thought I'd send a very simple example of how to plot
the solutions of the Lorenz system of differential equations
using "rk" and "gpdraw".
Of course, this owes much thanks to Jaime and Mario.
The enclosed file shows in a very meager sense the potential that
already exists for the study of nonlinear 3-d differential equations.
Just load the file "Lorenz.mac" and wait several seconds. On my dual
core linux system it takes around 5 seconds to produce the picture.
Once the picture is there, drag the left mouse button around, and then
move the middle mouse button left-right or up-down.
My students will like this!
Now, for some "wish list" items.
1. The keyboard is available. So, how about doing the rotations, and
zooms with combinations:
"r" key + left mouse
"z" key + middle mouse
or some such combination.
That leaves the left mouse key alone to allow selecting an initial
point in 3-space as a new initial condition to do real time plots of different
orbits. This is like what works in the "plotdf" 2d routine.
One could also implement some sort of menu (or dialog box) like
Jaime's in graph2d and plotdf. A special key could open a window
with commands, help, etc. I don't know what is preferable. One does
not want to make the program bloated.
The list could go on and on.
2. What about the name "draw" instead of "gpdraw"? Of course, with
aliases, this is not necessary.
-sen
P.S. The file "Lorenz.mac" is, of course, sort of trivial, and one
could do similar examples for most of the things in Maxima. So, if people
would prefer that such things not be sent to this development list, is there a more
appropriate place?
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| Sheldon E. Newhouse | e-mail: sen1 at math.msu.edu |
| Mathematics Department | |
| Michigan State University | telephone: 517-355-9684 |
| E. Lansing, MI 48824-1027 USA | FAX: 517-432-1562 |
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