Non Linear Diff EQ in astronomy

[chameleon68]

I'm trying to find a non-linear differential equation that relates to (preferably) Saturn or asteroids. I'm a grad student in mathematics and I'm part of a team that's built a mini differential analyzer. The mini only solves (up to) second order differential equations, but we're in the process of building a full size analyzer. My thesis will be using (possibly redesigning) the analyzer to solve a non-linear diff. eq. and I'd like to use a problem from astronomy that's relevant to the general public at the present time. The problem is that unlike most math students, I haven't taken any (okay maybe one) physics classes. I love science, but I don't 'do' it very well in classroom settings. So I'm hoping to gather some ideas from people who actually know something about the subject. Any ideas or even pointing me in a certain direction is greatly appreciated. I've searched (quite) a few journals and I've asked other people whom I work with for suggestions as well. I'd just like to get as much information as possible before deciding.

Thanks for any info!