A two-body orbit can be stable, assuming 'perfect gravitational spheres' (Newton), but for anything above that, or not perfectly symmetric, you will get a chaotic, non-linear solution as I understands it. The resonance I was talking about is simply the time it takes for an orbit around some center, so the Jovian satellite Io that makes a orbit in half the time of its brother Europa (roughly) has a resonance of 2 to 1 (expressed 2:1). For each orbit of Europe, Io makes two.