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ITSA General Assembly: December 5th - 12th

Author Topic: Gyros & Tops in space  (Read 6026 times)

ta0

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Re: Gyros & Tops in space
« Reply #30 on: July 08, 2019, 08:12:18 AM »

Merged with the previous thread.

What should a top spinner take on one of those airplane parabolic flights that simulate zero gravity for several seconds?  :-\
Not something I'm planning to do any time soon, but perhaps one day . . .
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Jeremy McCreary

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Re: Gyros & Tops in space
« Reply #31 on: July 08, 2019, 02:00:55 PM »

What should a top spinner take on one of those airplane parabolic flights that simulate zero gravity for several seconds?

You mean besides a barf bag?

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Iacopo

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Re: Gyros & Tops in space
« Reply #32 on: July 12, 2019, 11:56:43 AM »

I didn't know the T handle rotation behaviour.  I have been surprised looking at it.
It seems a sort of torque free precession, (which I don't understand how it works).
Amazing, anyway !
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Jeremy McCreary

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Re: Gyros & Tops in space
« Reply #33 on: July 12, 2019, 02:46:38 PM »

It seems a sort of torque free precession...

Yes, a very good approximation!

Aboard the ISS, the T-handle still experiences small torques due to microgravity and air resistance.The former's only a tiny fraction of the gravity we get here on the ground, but the drag's about the same.

The truly torque-free video simulation at the link I posted totally ignores these residual torques. Yet no visible departures from the T-handle's actual behavior over time windows without noticeable spin decay.

So in this case, the ISS environment is effectively torque-free. That makes a T-handle on the ISS a great demo of free precession of a rigid body with 3 different principal moments of inertia.
« Last Edit: July 12, 2019, 03:02:02 PM by Jeremy McCreary »
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ta0

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Re: Gyros & Tops in space
« Reply #34 on: July 12, 2019, 07:34:09 PM »

Iacopo: Below I copied my semi-intuitive explanation that I use to think about it. I'm curious if you find it helpful.

The most stable axis of rotation for an object is the one with largest (moment of) inertia. Although the axis with lowest inertia is also stable, if there is energy loss (e.g. air drag) it will eventually end up rotating along the maximum inertia axis. Imagine an object that is spinning unbalanced: the highest mass will tend to "fly out", thus aligning the rotation of the body with the axis perpendicular. 

The handle is spinning unstable and pulled towards spinning with the T paralllel to the wall, what correspond to the maximum moment of inertia. As it does this it has to slow down to maintain the momentum of rotation. But, as there is little friction the flipping overshoots like a pendulum that reaches the bottom and starts to climb up. The handle retraces its rotation in opposite direction, speeding up as the lower moment axis realigns itself with the momentum. And the same as the pendulum, when it reaches the same position on the other side, it will then "swing" back.

I guess that eventually air friction would settle it down into spinning slowly counter-clockwise with the T in a plane parallel to the wall.
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Iacopo

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Re: Gyros & Tops in space
« Reply #35 on: July 13, 2019, 02:20:57 AM »

Iacopo: Below I copied my semi-intuitive explanation that I use to think about it. I'm curious if you find it helpful.

The most stable axis of rotation for an object is the one with largest (moment of) inertia. Although the axis with lowest inertia is also stable, if there is energy loss (e.g. air drag) it will eventually end up rotating along the maximum inertia axis. Imagine an object that is spinning unbalanced: the highest mass will tend to "fly out", thus aligning the rotation of the body with the axis perpendicular. 

The handle is spinning unstable and pulled towards spinning with the T paralllel to the wall, what correspond to the maximum moment of inertia. As it does this it has to slow down to maintain the momentum of rotation. But, as there is little friction the flipping overshoots like a pendulum that reaches the bottom and starts to climb up. The handle retraces its rotation in opposite direction, speeding up as the lower moment axis realigns itself with the momentum. And the same as the pendulum, when it reaches the same position on the other side, it will then "swing" back.

I guess that eventually air friction would settle it down into spinning slowly counter-clockwise with the T in a plane parallel to the wall.

Yes, it helps understanding. It is well written. Thanks, Ta0.
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Jeremy McCreary

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Re: Gyros & Tops in space
« Reply #36 on: July 13, 2019, 05:20:35 AM »

The most stable axis of rotation for an object is the one with largest (moment of) inertia. Although the axis with lowest inertia is also stable, if there is energy loss (e.g. air drag) it will eventually end up rotating along the maximum inertia axis.

Nice description of dissipation-induced instability. Famous example: Explorer I, launched in 1958 to become the 1st US spacecraft to achieve orbit.

Plan A was to stabilize the attitude of this long, narrow rocket-shaped satellite by spinning it about its centerline. Would've worked in the absence of dissipation, as this was its axis of minimum moment of inertia. But by the end of its 1st orbit, Explorer I was no longer spinning like a bullet. Instead, it was spinning like a propeller about its axis of maximum moment of inertia, just as you described.

One teensy dissipation had been overlooked: Elastic heating of the 4 whip antennas as they flapped after release. Ultimately, the heat lost to space through the antennas took only a tiny bite out of the spacecraft's rotational kinetic energy. But that was all it took to switch Explorer I from bullet to propeller mode. Like the ISS T-handle, the spacecraft's total angular momentum changed very little in the mode switch. It just took on a different outward form.

An outside engineering professor familiar with this kind of instability tried to warn NASA months before launch, but security measures kept the heads-up from reaching project engineers. Seven months after launch, he published a paper spelling out the cause of the mode switch. Only then did the Explorer team tumble to what had happened.
« Last Edit: July 13, 2019, 07:57:13 PM by Jeremy McCreary »
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ta0

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Re: Gyros & Tops in space
« Reply #37 on: July 13, 2019, 02:35:09 PM »

I didn't know the Explorer I story. You would think that NASA's "rocket scientists" would have known better. That shows that rotational dynamics can be counter-intuitive.
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Jeremy McCreary

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Re: Gyros & Tops in space
« Reply #38 on: July 13, 2019, 03:04:45 PM »

I didn't know the Explorer I story. You would think that NASA's "rocket scientists" would have known better. That shows that rotational dynamics can be counter-intuitive.

Maybe they had an excuse. Examples of dissipation-induced instability turn out to be all around us, especially in nature. But the concept gained wide appreciation only in the 1990s -- just one of the many cool new insights to come out of the ongoing renaissance in classical mechanics.
« Last Edit: July 13, 2019, 07:59:23 PM by Jeremy McCreary »
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