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I have heard that an O'neill cylinder rotating about the central axis of the cylinder can be unstable. O'neill, himself, initially solved this problem by having two adjoining cylinders rotating in opposite directions.

Let's take a cylinder with R1 (the radius of the outer shell from the axis of rotation) to be 1050m, R2 (the radius of the inner shell to be 1000m and the length of the cylinder to be 3000m. Approximate the shell to be constant density (or evenly distributed mass). It will be in a constant tangential velocity orbit of the Earth.

I tried to learn the math of moment of inertia, but it baffled me. It seems to me that the axis with the higher moment of inertia would be the cylinder axis and so that the rotating cylinder would be stable. Could somebody do the math for me? Does the stability vary with the length to diameter ratio of the cylinder?

Jack R. Woods
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  • This topic is covered in the physics and space sections of SE. See for example https://space.stackexchange.com/questions/2731/what-stability-issues-plague-long-artificial-gravity-cylinders – almagest Sep 22 '19 at 06:18
  • Still not seeing the math. The Kalapana One article gives a maximum length to radius ratio of 1.3, but the other reference shows a wobble frequency proportional to (m/M)^2, g^1/2, d^2 and R^-5/2 (where g = 10m/s if Earth gravity, m and d are the mass and distance moved of a disturbing object, M is the mass of the ship and R is the radius of the ship). Also given is that the wobble amplitude is proportional to md/M. d/R and m/M can be quite small for a large cylinder. It seems to me that the Kalapana One article oversimplifies and that a stability correcting mechanism may fix this problem. – Jack R. Woods Sep 23 '19 at 16:28

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