1. Does orienting the long direction of the modules in-plane with the rotation provide enough moment of inertia on the intermediate axis to avoid the risk of oscillation? See .
Conceivably, one might repurpose the High Frontier physics engine to evaluate that type of stability. Model the geometry in the simulation except spin it sideways (cylinder axes parallel to spin axis), and see how long it takes to damp the oscillation as it falls into the lower energy state (cylinder axes perpendicular to spin axis).
One easy hack is to put solar arrays in-plane with the rotation, eg Vast.
2. For the spin-up procedure, it seems easier to start by spinning up the connected modules, then spooling out the tether gradually. This avoids the "bounce" problem entirely. By controlling the rate of unspooling and thruster firing, a suitably gravity level can be maintained during deployment.
Thanks, very interesting proposal!
Edit to add: three apparently...
3. With all the cables coplanar, you will likely encounter an undesirable "twisting" oscillation. This can be fixed by putting some of the cables out-of-plane with each other.
One approach would be to add a big truss to the top of the cylinders that juts out sideways, and run cables to the ends of that. Sounds heavy.
A more light-weight approach uses tensegrity. Add a single central "floating" rod in compression (colinear with the spin axis) and have cables run from each end of the rod to each end of the cylinder. Minimally there would be four cables which form a long thin tetrahedron. For redundancy, probably four cables per end.
A longer rod gives more stability but adds more mass, so it's a typical tradeoff.