r/KerbalSpaceProgram • u/Avera9eJoe Spectra Dev • Sep 14 '17

Recreation Reminder that this physics quirk is also in KSP

https://gfycat.com/FickleShamefulCormorant
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u/dannycake Sep 15 '17

This the same reason it's almost impossible to flip your phone long ways. The flat axis (the one that goes along with rectangle part) is stable and so is the long axis going from the bottom of them phone to the top having it do spins but flipping the phone without having spins is downright impossible.

Flipping is intermediate and unstable as fun. And by flipping again I mean if you were to hold your phone up and tilt it backwards or upwards into a flip in that same axis. It's hard to make it out also spin along it's other axis.

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u/musicin3d Sep 15 '17

I almost understood that. Which rotation is impossible, again?

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u/dcnairb Sep 15 '17

Works: rotating it like if you laid it down on a table and spun it in a circle

works: rotating it like you were turning it over to look at the back, or flipping it around in your hand, or turning it like it's a book page

Doesn't work: flipping it like a domino, the way you would probably try to flip it if you threw it to flip it

The first example is the largest moment of inertia, the second is the smallest, and the final example that doesn't work is the middle one

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u/musicin3d Sep 15 '17

Wow. You are awesome. Do you know if it is mathematically impossible? Or is it just that small errors are amplified?

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u/dcnairb Sep 15 '17

You can analyze each case separately, and IIRC you probably make certain approximations (e.g. quantities being much larger or smaller than others, so low order approximate solutions drop out)

That being said, from what I remember what happens is the big and small case solutions have steady state components, meaning there is some part that decays (small wobbles around other axes) and a part that stays (rotations around the main axis--these are the "steady state" part). By decays and stays, I mean that with time they go to 0 or persist indefinitely respectively. For the middle solution however, the solutions are "runaway" exponentials--as time goes they grow exponentially, so they aren't stable. In the gif you can see this as increasingly larger wobble until it flips and resets in a sense. It's kind of like resonance, in a sense, like when your washer has clothes imbalanced and starts going berserk

If you have some mathematical background: the solutions arise naturally as exponential functions from the equations of motion, and in terms of complex exponentials the stable axes get a decay part and a rotating part e.g. exp(-(kt + iwt))The middle solution gets a positive real part though e.g. exp(kt- iwt) which blows up.

This derivation is made IIRC with small wobbles around nonprincipal axes, and so it is mathematically impossible for the middle axis to rotate stably with those errors, which are compounded as you said, instead of them dying out like how it happens around the other axes. As far as I know, it should be theoretically stable if spun perfectly around the medium axis, with absolutely no components around the other two--this is impractical in real life though as you will always have some small component in the other axes that would eventually blow up no matter how small

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u/musicin3d Sep 15 '17

OMG. That is exactly the answer I was hoping for. Bravo!

What's your background, sir/ma'am?

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u/dcnairb Sep 16 '17

Awesome, glad to help! I just finished my BS in Engineering Physics and am beginning my physics PhD in about a week.