I work with an electromagnetic molecule trap, and I'd like to determine which orbits are chaotic. To this end, I intend to study the evolution of a perturbation on a trajectory with time. I'd like to compute something called the fast lyapunov indicator for various trajectories y(t), where I have a force law y''(t)=f(y). I'm told I need to consider a variation dy, and follow its evolution d(dy)/dt = df(y)/dy * dy. My questions are: 1. how do I deal with the fact that I have a second order equation not first. 2. Could I just evolve two trajectories separated by dy initially in order to evolve dy, or is this much less precise than evolving dy according to its specific higher order evolution equation?