How do higher numbers affect orbital resonance? is a really interesting question, and I thought I would try to do a simple numerical simulation of various resonance ratios to see if some are inherently stable or inherently unstable.
I understand that numerical simulation is inexact and so it can introduce its own instabilities so attention will have to be paid to the choice of integrators and results taken with a large grain of salt.
In order to get something to happen within say a hundred or a thousand orbits the masses of the orbiting bodies have to be large enough to have a significant impact on each other1, and so the state vectors I choose to initialize the calculation will not necessarily be those of circular orbits each body neglecting the other.
Are there any guidelines or rules of thumbs for initializing resonant orbits?
1I'll assume a central force, i.e. the orbiting bodies will not affect the position of the body they orbit, and so there won't be any indirect coupling through it.