Program calculating bounces of a particle off circles.

[firegoalie33]

Homework Statement

Okay. So my goal is to bounce a particle off of 3 circles with centers at the vertices of an equilateral triangle. The side length of each side of the triangle is 6 units and the radius of the circles are 1 unit. I am shooting a particle from anywhere at any angle with unit speed. The particle needs to bounce around in the system of circles and eventually escape. I have written a computer program to model this behavior. I am NOT allowed to shoot it in a manner that creates an infinite number of bounces.

Homework Equations

Does anyone have a hunch as to what starting location and starting angle i should use to get the highest number of hits?

The Attempt at a Solution

The most i can get is three. and this was done using random numbers in the computer.

 

[zhermes]

If there actually exists an analytic way to get an infinite number of bounces, I would suspect that you can also achieve any arbitrarily high number of bounces depending on your machine accuracy.

I.e. If some trajectory yields an infinite number of bounces, then a tiny perturbation from that trajectory should yield a very large number of bounces, and progressively smaller perturbations will yield arbitrarily high numbers of bounces.

 

[Borek]

I am with zhermes here - start with shot that should generate infinite bounces, modify the angle by any amount - the smaller the better.