🚀 go-pugleaf

Hi -- I realized that I wasn't very clear in my first posting, so I'm
going to try again.

I'm working on a project involving billiard balls in a convex space,
i.e., an ellipse, stadium, circle, etc.  Currently, my program just
calculates the trajectory (given an initial velocity and position).
When the ball collides with a wall, the angle of incidence = angle of 
reflection.  There's no gravity, not acceleration in fact, and no
spin.  I do realize that this problem is pretty much deterministic.

However, even though it may be deterministic, I think that the
lyapunov exponents for the ellipse and stadium are positive (and 0 for
the circle), and I want to calculate them.

My current implementation is to take two points with slightly
different starting points, iterate them through the system, and
calculate the "x" and "y" exponents. i.e., 
l_x = 1/n sum( log_2 d_(i+1)_x - d_i_x )
                    --------------------
			d_i_x
where d_i_x = separation between the 2 pts at the ith iteration.

The problem with this implementation is that the direction of the
largest change is probably not in the x or y direction.

Alternatively, I could just calculate the largest exponent (just do
the total change), but I would really like to be able to get two
exponents.


Any ideas, suggestions, references, etc.?

Thanks a lot in advance!

-- Diane
dtang@husc.harvard.edu