Is Rama stable?

[Dorfl]

Could a long rotating cylindrical space station keep rotating around its lengthwise axis without active stabilisation?

Last semester a teacher briefly mentioned a cylindrical satellite which unexpectedly began wobbling after a while, and eventually switched to rotating around an axis going through its sides, instead of the endpoints. When I read Rama slightly later, I didn't reflect over it, but this comic reminded me again.

Of course, the Ramans probably wouldn't have any problems keeping Rama stable, if they wanted to.

 

[drkitten]

Could a long rotating cylindrical space station keep rotating around its lengthwise axis without active stabilisation?

Probably not. Butterfly effect and all that.

[I believe that] A cylinder rotating around its long axis is "metastable," in the same way that a cone resting on its vertex is. If it were balanced perfectly there would be no particular reason why it would fall one way instead of another, and so would remain there until something broke the symmetry.

Something like, oh, say, a passing micrometeorite. Or movement inside the station as everyone goes to the north end for a baseball game. Or quantum-scale fluctuations.

 

[Doubt]

This problem was addressed in "Ringworld Engineers".

Larry Niven did not take the stability in the plane of rotation into account in his first Ringworld book. When fans pointed out the issue to him it became the source of the plot for the second book.

 

[Floyt]

Isn't Rama self-propelled? If so, there probably are attitude adjustor jets. Needn't be quite in the harnessed solar flare range either...

 

[dudalb]

This problem was addressed in "Ringworld Engineers".

Larry Niven did not take the stability in the plane of rotation into account in his first Ringworld book. When fans pointed out the issue to him it became the source of the plot for the second book.

I know several people who were there when people stood outside Niven;s balcony window at a hotel where a Sci Fi Con was being held chanting "the Ringworld is unstable!The Ringworld is unstable" in unison.......

 

[dasmiller]

Could a long rotating cylindrical space station keep rotating around its lengthwise axis without active stabilisation?

Now we're on my turf! No, assuming any vaguely smooth mass distribution, Rama wouldn't be passively stable about the spin axis. You could come up with mass distributions that would be (a very heavy hoop in the center, with the rest very lightweight), but I don't think Clarke gave us any indication of that.

Last semester a teacher briefly mentioned a cylindrical satellite which unexpectedly began wobbling after a while, and eventually switched to rotating around an axis going through its sides, instead of the endpoints. When I read Rama slightly later, I didn't reflect over it, but this comic reminded me again.

We generally refer to that as "tumbling" or "going into a flat spin." Offhand, I know of only one spacecraft that was lost that way, though of course there have been a lot of spinning spacecraft that required active stabilization, and once the spacecraft is retired, the 'active' part stops so presumably there are a lot of tumbling spacecraft slightly above the GEO belt.

Of course, the Ramans probably wouldn't have any problems keeping Rama stable, if they wanted to.

There are a number of ways to stabilize a spinner, yes. Of course, we'd prefer not to use thrusters, but there are tricks with moving masses. If Rama had a big hunk of mass spinning at a different rate, then there are all sorts of games one can play.

 

[sol invictus]

[I believe that] A cylinder rotating around its long axis is "metastable," in the same way that a cone resting on its vertex is.

That's not metastable (unless the vertex is flattened or concave). Metastable means locally stable but globally unstable, like a ball in a bowl suspended over the floor.

Now we're on my turf! No, assuming any vaguely smooth mass distribution, Rama wouldn't be passively stable about the spin axis. You could come up with mass distributions that would be (a very heavy hoop in the center, with the rest very lightweight), but I don't think Clarke gave us any indication of that.

I thought rigid bodies were stable under rotations around the principal axes with the largest and smallest moments, and unstable around the intermediate one. The long axis (for a long cylinder) is the one with the smallest moment, so why isn't the rotation stable?

 

[BoogieWoogieWookie]

I thought rigid bodies were stable under rotations around the principal axes with the largest and smallest moments, and unstable around the intermediate one. The long axis (for a long cylinder) is the one with the smallest moment, so why isn't the rotation stable?

That is my understanding also. I have all four of the Rama books and I have read each of them three times. I have a solid mental picture of the spacecraft thanks to Clark's clear and vivid descriptions of them.

The spacecraft is described as a cylinder 54 km long and 20 km in diameter that rotates around its long axis to create artificial gravity along its inside curved walls. It has cities and even a sea along these curved walls which would be impossible, of course, if the craft rotated end-over-end style.

 

[Brian-M]

If the mass is distributed evenly... and compartmentalised so it can't become unevenly distributed over time, how could it possibly become unstable?

This isn't a rhetorical question... I genuinely want to know.

 

[nathan]

Could a long rotating cylindrical space station keep rotating around its lengthwise axis without active stabilisation?

no

Last semester a teacher briefly mentioned a cylindrical satellite which unexpectedly began wobbling after a while, and eventually switched to rotating around an axis going through its sides, instead of the endpoints. .

Right, I was taught the same lesson at university. The reason given was that real-world cylinders are not perfectly rigid. Internal flexing allows the axis of rotation to migrate. This happens with artificial satellites, and it apparently was a surprise when the first such cylindrical satellite did it.

 

[Dorfl]

Isn't Rama self-propelled? If so, there probably are attitude adjustor jets. Needn't be quite in the harnessed solar flare range either...

I'm not sure. I'd imagined it as being basically in stand-by, once it's bounced off of a star. Maybe it still has some small space-warpey adjusters active when travelling, though.

 

[Dorfl]

Right, I was taught the same lesson at university. The reason given was that real-world cylinders are not perfectly rigid. Internal flexing allows the axis of rotation to migrate. This happens with artificial satellites, and it apparently was a surprise when the first such cylindrical satellite did it.

Hmm... Would a perfectly rigid cylinder keep spinning around the right axis, even while being pelted by micrometeorites and stuff?

 

[Dorfl]

Now we're on my turf! No, assuming any vaguely smooth mass distribution, Rama wouldn't be passively stable about the spin axis. You could come up with mass distributions that would be (a very heavy hoop in the center, with the rest very lightweight), but I don't think Clarke gave us any indication of that.

Me neither. I guess a hoop could be fitted into either of the walls at the ends, but the interior of the ship is supposed to be empty.

We generally refer to that as "tumbling" or "going into a flat spin." Offhand, I know of only one spacecraft that was lost that way, though of course there have been a lot of spinning spacecraft that required active stabilization, and once the spacecraft is retired, the 'active' part stops so presumably there are a lot of tumbling spacecraft slightly above the GEO belt.

I guess people tend not to make the same mistake twice, when handling multi-million dollar spacecraft. Hmm... If parts break off of a satellite, is it more or less likely to produce dangerous space debris if that satellite is spinning?

There are a number of ways to stabilize a spinner, yes. Of course, we'd prefer not to use thrusters, but there are tricks with moving masses. If Rama had a big hunk of mass spinning at a different rate, then there are all sorts of games one can play.

So it could be made passively stable? Since it seems to be implied that Rama is pretty much inactive when not near a star.

 

[nathan]

Hmm... Would a perfectly rigid cylinder keep spinning around the right axis, even while being pelted by micrometeorites and stuff?

no. then there's an external source of torque. It'd depend on the distribution of the micrometeorites as to whether the axis wandered randomly or not though.

ETA:

I've realized a confusion here. With the external torque, the axis of rotation can now wander around the celestial sphere. Without that torque (as I'd read the original question), the axis remains fixed against the celestial sphere. With a non-rigid cylinder, the axis can wander relative to the cylinder's axes, with a rigid cylinder it cannot.

So, to be specific. With an isolated non-rigid cylinder, whatever star happens to be 'the pole star', will remain so, but the point on the surface of the cylinder directly below that pole star will change. Until the cylinder has reached the stable equilibrium of rotating around its highest inertial axis (at the lowest angular velocity).

At least that's my understanding, which is consistent with conservation of angular momentum.

 

[sol invictus]

With a non-rigid cylinder, the axis can wander relative to the cylinder's axes, with a rigid cylinder it cannot.

Rigid objects have two stable principal axes of rotation and one unstable. If you start with a rotation around the unstable axis, any tiny deviation (either in the initial condition or caused by some infinitesimal torque) will cause the rate of rotation about the other axes to grow exponentially (note that this does not mean the angular momentum is changing - it's actually a consequence of the fact that it's not changing).

On the contrary if you start with a rotation around either of the two stable axes, the perturbation doesn't grow. The long axis of a cylinder is one of the stable axes.

The non-rigid case is another matter, which sounds interesting.

 

[nathan]

Rigid objects have two stable principal axes of rotation and one unstable. If you start with a rotation around the unstable axis, any tiny deviation (either in the initial condition or caused by some infinitesimal torque) will cause the rate of rotation about the other axes to grow exponentially (note that this does not mean the angular momentum is changing - it's actually a consequence of the fact that it's not changing).

yeah, you're right. I'd got hung up about rotating the cylinder about its principle axes and forgot about other possibilities.

 

[Dorfl]

Rigid objects have two stable principal axes of rotation and one unstable. If you start with a rotation around the unstable axis, any tiny deviation (either in the initial condition or caused by some infinitesimal torque) will cause the rate of rotation about the other axes to grow exponentially (note that this does not mean the angular momentum is changing - it's actually a consequence of the fact that it's not changing).

Is this true even in the case of a cylinder?

 

[sol invictus]

Is this true even in the case of a cylinder?

Let me preface this by saying that I haven't thought about this kind of thing in a long time, so I might be wrong. But here's how I remember it: given an arbitrary rigid body you start by computing the moment of inertial tensor. It's real and symmetric, hence you can always diagonalize it. Do so. With the origin on the center of mass, the three basis vectors are the three principal axes, and their eigenvalues are their moments.

Then, as I remember it the one in the middle is unstable, and the two with max and min moments are stable. For a cylinder two are equal and one (the long one) is different; therefore the long one can never be the one in the middle; therefore it should be stable.

 

[Dorfl]

Let me preface this by saying that I haven't thought about this kind of thing in a long time, so I might be wrong. But here's how I remember it: given an arbitrary rigid body you start by computing the moment of inertial tensor. It's real and symmetric, hence you can always diagonalize it. With the origin on the center of mass, the three vectors in that basis are the three principal axes, and their eigenvalues are their moments.

Uh... I think we'll read about tensors next year, so for now I'll take your word for it.

Then, as I remember it the one in the middle is unstable, and the two with max and min moments are stable. For a cylinder two are equal and one (the long one) is different; therefore the long one can never be the one in the middle; therefore it should be stable.

That sounds reasonable. So a cylinder has to be non-rigid to spontaneously switch from the length-wise axis?

 

[sol invictus]

Uh... I think we'll read about tensors next year, so for now I'll take your word for it.

Just think of it as a 3X3 matrix.

That sounds reasonable. So a cylinder has to be non-rigid to spontaneously switch from the length-wise axis?

I think so, but I could be wrong.