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Author Topic: Gyros & Tops in space  (Read 7557 times)

cecil

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Tops in Space
« Reply #15 on: October 18, 2016, 05:52:10 PM »

https://youtu.be/Df-Jhnemhes

Me and Rosie got to try space.
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ta0

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Re: Gyros & Tops in space
« Reply #16 on: October 18, 2016, 11:17:07 PM »

Thanks for re-posting this video, Cecil.
It is very relevant to the discussion we are having now about the behavior of an unbalanced top.
I agree with the astronaut: I would have expected the unbalance top to wobble much more that it does!  ???
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Russpin

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Re: Gyros & Tops in space
« Reply #17 on: October 22, 2016, 12:01:38 PM »

It is very relevant to the discussion we are having now about the behavior of an unbalanced top.
I agree with the astronaut: I would have expected the unbalance top to wobble much more that it does!  ???

If you model the top as a thin disk of radius r and mass of m and put a point mass of mp at the rim. The center of mass is then at distance of r*mp/(m + mp) from the center of the disk along a line from the center of the disk to the point mass on the rim. Letting this line be the body x axis and the line perpendicular to it in the plane of the disk be the body y axis. The body z axis is then perpendicular to the plane of the disk. The moments of inertia about this center of mass are:

Ix = 0.25*m*r^2
Iy = (.25*m + m*mp/(m + mp))*r^2
Iz = (.5*m + m*mp/(m + mp))*r^2

It's important to note that these are the principal moments of inertia and the x,y and z axes are the principal axes of inertia. It's seen that:

Ix < Iy < Iz

The intermediate axis theorem states that rotation about the minimum or the maximum principal axes is stable. While rotation about the intermediate axis is unstable. In the video she spins the top about the z axis which is the maximum moment of inertia and so is stable.

I made a animation of the intermediate axis theorem here:

https://www.youtube.com/watch?v=-2cMmwIKTJM
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ta0

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Re: Gyros & Tops in space
« Reply #18 on: October 22, 2016, 01:39:31 PM »


The intermediate axis theorem states that rotation about the minimum or the maximum principal axes is stable. While rotation about the intermediate axis is unstable. In the video she spins the top about the z axis which is the maximum moment of inertia and so is stable.

I made a animation of the intermediate axis theorem here:


Very nice!
We have discussed this before. Here is a finger top I have, made by Philippe Dyon from France:



It refuses to spin on the dark axis but spins well on the other two, even though the three are axis of radial symmetry. Philippe makes the dark axis of a heavier wood on purpose to demonstrate the effect.

You should enjoy this quiz we had a while back: http://www.ta0.com/forum/index.php/topic,717.0.html
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Russpin

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Re: Gyros & Tops in space
« Reply #19 on: October 22, 2016, 02:01:27 PM »

You should enjoy this quiz we had a while back: http://www.ta0.com/forum/index.php/topic,717.0.html

That's a neat contest. The big X (#24) fooled me also. I thought it would spin for sure.
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ta0

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Re: Gyros & Tops in space
« Reply #20 on: October 22, 2016, 08:49:57 PM »

You should enjoy this quiz we had a while back: http://www.ta0.com/forum/index.php/topic,717.0.html

That's a neat contest. The big X (#24) fooled me also. I thought it would spin for sure.

Now you have to simulate what may be the most amazing rotational movement, the T-Handle flip:o

« Last Edit: October 26, 2016, 12:33:22 AM by ta0 »
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Russpin

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Re: Gyros & Tops in space
« Reply #21 on: October 23, 2016, 08:34:03 AM »

Now you have to simulate what may be the most amazing rotational movement, the T-Handle flip!  :o
http://www.ta0.com/forum/index.php/topic,3966.msg40906.html#msg40906

This looks like rotation about the intermediate principal axis. If you watch my video closely the rigid body flips the same way, only slower.

https://www.youtube.com/watch?v=-2cMmwIKTJM
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ta0

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Re: Gyros & Tops in space
« Reply #22 on: October 23, 2016, 11:04:24 AM »

Now you have to simulate what may be the most amazing rotational movement, the T-Handle flip!  :o
http://www.ta0.com/forum/index.php/topic,3966.msg40906.html#msg40906

This looks like rotation about the intermediate principal axis. If you watch my video closely the rigid body flips the same way, only slower.


You are right, it looks very much the same. But I think that the colors of the faces are more difficult to follow than something projecting out of the face. I imagine it should be easy to model the T-handle instead of a brick. Then you can do a presentation showing the Nasa video together with the simulation.  ;)
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Russpin

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Re: Gyros & Tops in space
« Reply #23 on: October 23, 2016, 01:37:55 PM »

I imagine it should be easy to model the T-handle instead of a brick. Then you can do a presentation showing the Nasa video together with the simulation.  ;)

The hardest part would be calculating the principal moments of inertia for the T-handle.
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Russpin

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Re: Gyros & Tops in space
« Reply #24 on: October 25, 2016, 05:59:36 PM »

I got curious about the effect of different intermediate moments of inertia on the motion of the T handle. The following animation shows the motion for Ix = 3.5, 3.7 and 3.9 with an initial angular velocity of 2.5 rad/s along the x axis. Iy and Iz moments of inertia were held fixed at 3.43 and 3.95 respectively.
https://www.youtube.com/watch?v=KkEN9T0YUCY
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ta0

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Re: Gyros & Tops in space
« Reply #25 on: October 26, 2016, 12:24:44 AM »

Wonderful! I love these animations! I can see them becoming classics in the classroom!

It seems pretty clear comparing the three cases that the instability is stronger the more "intermediate" is the intermediate moment of inertia.

Something that the casual observer may not realize is that the handle reverses the direction it spins with respect to the key. For example, it would close a door when facing right but open it when facing left. Perhaps you could add some color bands or "paint" arrows to make it obvious.

Great work!

EDIT: I merged this thread with the one with the T-handle video.
« Last Edit: October 26, 2016, 01:22:13 PM by ta0 »
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Jeremy McCreary

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Re: Gyros & Tops in space
« Reply #26 on: October 26, 2016, 10:02:23 AM »

Very impressive simulations, Russpin! What programming language or software do you use?
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Playing with the physical world through LEGO

Russpin

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Re: Gyros & Tops in space
« Reply #27 on: October 26, 2016, 10:42:43 AM »

Very impressive simulations, Russpin! What programming language or software do you use?

I wrote the simulation in Python and the animation was done in Blender.
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Renee

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Spinning T-handle in zero-g
« Reply #28 on: July 07, 2019, 01:36:40 PM »

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Jeremy McCreary

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Re: Spinning T-handle in zero-g
« Reply #29 on: July 08, 2019, 02:19:08 AM »

Very cool. A good explanation and video simulation...

https://rotations.berkeley.edu/a-tumbling-t-handle-in-space
« Last Edit: July 12, 2019, 07:42:52 PM by Jeremy McCreary »
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