March 17, 2004
Billiards Software
Steven Lansel is conituing to develop his Billiards software, a project he started in the Summer 2003 REU program.
A Billiard system is a ball that is moving around some table, though the table ispermitted, in general, to have a very complicated geometry. There is an explanation from a master of the subject, Yakov Sinai available.
It is a famous theorem of Professor Bunimovich that if the table has the shape of a soccer stadium, so a rectangle, with a semi circle on each end, that the movement of a billiard ball is generically chaotic. This chaotic behavior is also the case of mushrooms: A semi circle centered on top of a rectangle.
The picture shown here is of a much more complicated geometry, with
an ellipse stuck on top of a rectangle. In particular, Steven is currently looking at a generalization of Bunimovich's mushroom billiard in which the cap of the mushroom is
elliptical rather than circular. (The extra complexity in this system
arises from the fact that the integrable elliptical billiard has two kinds of
caustics, whereas the circular billiard has just one.) Steven's program
will prove very useful in studying this both for numerical experiments and
to help guide analytical work. We are at the beginning stages of this and
have been discussing this with Lyonia.
The current version of the code can be downloaded either from my research
website (www.math.gatech.edu/~mason/research/new.html) or from Steven's
billiard website (http://lansel.no-ip.com/billiards2/). Steven's website
also shows plots and includes example data sets that can be downloaded for
your viewing pleasure.