Rotating bodies in microgravity

[RainDreamer]

So why does they spin the way they do? Solid body spin stably. Liquid filled body spin unstably, unless in a long cylinder object. Since I am not exactly a physics student, I just know it has something to do with inertia, but not more. Can anyone explaining it in layman terms?

[insert_name]

probably has to do with as the liquid container spins its center of mass shifts

[sevenperforce]

insert_name is right. All objects have a center of mass, and solid objects can spin stably on any axis passing through that center of mass as long as the angular momentum around that axis is maintained. However, with a liquid-filled object, the centrifugal forces caused by spinning produce internal forces on the liquid, causing it to circulate. The circulation transfers angular momentum away from the spin axis, producing a new spin axis, which produces additional force, further misaligning the spin axis. Plus, if there are bubbles in the liquid, this can also alter the center of mass, further messing things up.

With the long cylinder, the liquid still circulates, but the shape of the body causes it to circulate in perfect alignment with the spin axis, so there is no misalignment and no shift in angular momentum.

[micr0wave]

this one is also interesting

someone built that in KSP, but i can't find the video to it.

[magnemoe]

5 minutes ago, micr0wave said:

this one is also interesting

someone built that in KSP, but i can't find the video to it.

That one is weirder, I guess the air bobbles in liquid forces them center of gravity to change, this changes rotation who moves the bubbles and change it again, it then reach an point where the bobbles are close to center and keep rotation for some time until unbalance build up. 

[K^2]

2 hours ago, sevenperforce said:

insert_name is right. All objects have a center of mass, and solid objects can spin stably on any axis passing through that center of mass as long as the angular momentum around that axis is maintained.

That isn't correct, either. Solid objects can only have a stable spin around one of the principal axes. There are typically just three that are mutually orthogonal, unless there is a degeneracy. An example of a fully degenerate solid body is a sphere, which can have a stable spin around any axis through its center of mass. But take something like a brick, and it will only have a stable spin through the three axes that exit perpendicular to the brick's surface.

Rotation around any other axis results in what is called axis tumbling. It's a periodic precession of the rotation axis around one of the principal axes. While it looks fairly stable in most configurations, there are some rather extreme counterexamples. Note that what you are seeing is a rigid object, with no flex or sloshing responsible for this motion. It does, however, have two axes with very high moment of inertia, and one axis with very small moment of inertia. The short peg sticking out of the handle breaks symmetry just enough to prevent the two large moments from being degenerate, and initial spin axis is just a hair short of being perfectly aligned with the slightly smaller moment of inertia principal axis.

This is pretty unique combination of rigid body configuration and initial conditions, and it results in rather unique motion. I hope this example is sufficient to convince you that rigid body spin stability isn't quite as simple as it sounds at first.

[Yourself]

6 hours ago, K^2 said:

But take something like a brick, and it will only have a stable spin through the three axes that exit perpendicular to the brick's surface.

The rotation is only stable around 2 of the principal axes if each of the principal moments is distinct (the axes with the minimum and maximum moments of inertia will be stable, while the one with the intermediate moment will not be). This is described by the tennis racket theorem.

The rotation of the book at the beginning of the video demonstrates this.  The first two rotations shown are about the stable axes, while the third shown is the unstable one (since the book tumbles over a half turn every so often.

 

[Streetwind]

10 hours ago, magnemoe said:

That one is weirder, I guess the air bobbles in liquid forces them center of gravity to change, this changes rotation who moves the bubbles and change it again, it then reach an point where the bobbles are close to center and keep rotation for some time until unbalance build up. 

The thing with the T-shape is actually a simple but highly unintuitive result of conservation of momentum. That's why you can recreate it in KSP with good accuracy.

Edited March 1, 2016 by Streetwind

[K^2]

3 hours ago, Yourself said:

The rotation is only stable around 2 of the principal axes if each of the principal moments is distinct (the axes with the minimum and maximum moments of inertia will be stable, while the one with the intermediate moment will not be). This is described by the tennis racket theorem.

The rotation of the book at the beginning of the video demonstrates this.  The first two rotations shown are about the stable axes, while the third shown is the unstable one (since the book tumbles over a half turn every so often.

Now we're getting into finer points of what we call stable. The intermediate axis is still an eigen vector of the moment of inertia tensor. L = I₂ω, so if L' = 0, then ω' = 0. The fun stuff happens when your axis of rotation is a tiny bit deflected from the intermediate axis. That's when you get a tumble. If we were looking at it from perspective of EQMs on ω in phase space, I'd call it an unstable equilibrium. But in that case, I'd have to call tumbling itself a stable orbit on ω, which is all sorts of confusing. When we talk about axis stability, we usually talk about lack of precession, rather than stability with respect to perturbation. By that measure, all three axes are stable. But if you're an engineer, and you're just trying to build a flywheel that doesn't wobble, all you care about is that any perturbation on ω die out. And that leaves you with just two good options.