[Edu-sig] More preaching to the choir...

[Edward Cherlin]

2008/10/19 kirby urner <kirby.urner at gmail.com>:
>
>
> Here's a pointer to some related writings @ Math Forum, which I used to tell
> Arthur S. (this archive) was more like "center ring" in my circus, i.e.
> where math teachers meet irrespective of caring about geek subculture,
> computers etc.:
>
> http://mathforum.org/kb/thread.jspa?threadID=1845616&tstart=0
>
> Re planets in orbit, another interesting implementation, already field
> tested, multiplies complex numbers of unit radius, begetting rotation, then
> scales appropriately.  Of course these orbits are merely circular, so not
> that realistic, so apply some field distortion if wanting elliptic (not
> something we tried).

I did a simulation of elliptical orbits in TutSim on the Apple II in
1982. It isn't that hard. I know of several different ways of
programming it, using inverse-square gravity, Kepler's law of equal
areas, and other equivalent mathematical representations. I set up a
three-body simulation in which one object was thrown out and the other
two settled into elliptical orbits around their barycenter, after a
chaotic early period. There are such simulations in a number of
languages, including Python and Smalltalk, where students can vary
parameters and watch the results. Some of this is in the Sugar
software for the OLPC XO.

A. K. Dewdney's book The Planiverse describes simulations of inverse
linear gravity in 2D, and others have done inverse cube gravity in 4D.
You can get weird weather, seasons, and climate effects on planets in
4D with two independent axes of rotation, depending in particular on
whether the rotation periods and the revolution period are close to or
far from simple integer ratios.

> Here's some code:
> http://www.4dsolutions.net/ocn/python/orbits.py
>
> Kirby
> 4D
>
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>



-- 
Edward Mokurai Cherlin
http://wiki.sugarlabs.org/go/User:Mokurai
http://www.amazon.com/xo
Give One, Get One, from Nov. 17