Toroidal planetary systems.

Question

Is it possible that two toroidal, rigid, homogeneous planets are forming a system in which the toroids are chained through each other, and during their mutual motion, the planets are never touching each other? How should I go about studying the systems of the above kind, and classify them according to their geometrical parameters, masses and initial dynamical parameters.

 Are there systems which are stable? (I considered the fact that there are a sizeable number of dynamical degrees of freedom.) What happens in the case for example, if the ‘orbit’ frequency reduces a bit, or if the plane of one of the toroids tilts slightly?

 (I'm aware that Analytic calculations are favorable. For numerical calculations, the results should be cross-checked in some semi-analytic way, what would that be?)

Comments

I think you should first check numerically whether what you describe is feasible and seems to be stable. This will be much simpler than the analysis that would prove this. 

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@Arnold Neumaier Yeah, as you have mentioned numerical analysis is quite easy, I'm struggling with the mathematical modelling part. It would be of great help if you could suggest how to go about analysing such a system.

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In this case I think you should report (or refer to a pdf file) in your question about the model employed and what the numerical study suggests. If you have a seemingly stable approximate solution, one can possibly create a computer-assisted proof establishing a true solution nearby. But don't expect it to be easy.