iTopSpin

Current Posts => Collecting, Modding, Turning and Spin Science => Topic started by: ta0 on October 16, 2013, 05:28:31 PM

Title: Gyros & Tops in space
Post by: ta0 on October 16, 2013, 05:28:31 PM
Here is Chinese astronaut (or taikonaut) Wang Yaping demonstrating the gyroscope effect last June.

Wang Yaping demonstrates gyroscopic motion in space (http://www.youtube.com/watch?v=LhlvK6iW50Y#)

I wouldn't mind getting lost in space with her  :D

By the way, I saw (in 3D) the recently released movie Gravity and it is very good.  There are no actual spinning tops but there is lots of spinning.  It is in fact a lesson on angular momentum.  I would have just changed one scene: when the two main (~ only) characters are separated.  It is physically wrong (most of the movie gets the physics right) and I have a solution that would have worked even better for the drama.  Anyways, I highly recommend it.
Title: Re: Gyros & Tops in space
Post by: ta0 on October 16, 2013, 11:08:52 PM
And here an American astronaut (Petit ?) showing gyroscopic stabilization using CD players:

Gyroscope behavior in low gravity. (http://www.youtube.com/watch?v=kCyMZFwb_O8#)
Title: Re: Gyros & Tops in space
Post by: ta0 on October 17, 2013, 11:33:53 AM
Something hit me this morning when I was still in bed.  On the last video the astronaut seems to not understand what happens when you add more that one gyroscope ! :o What is much more surprising is that nobody in NASA told him!  :o  ???  Perhaps he designed the demonstration without outside vetting and this was broadcasted live so now it lives in youtube and NASA cannot take it back  :-\ 

If you add two gyroscopes at 90 degrees to each other, it is equivalent to a single gyroscope aligned along the middle (bisector, if they are spinning in the "same" sense).  The thing would still be able to rotate around this axis and the stabilization would be less than stacking the two CD players on top of each other.  The reason is that along the perpendicular axis the rotation of the two CD players cancel each other (like two gyros spinning in opposite directions cancel each other).

When he added the 3 CDs at 90 degrees to each other he just got the equivalent to one aligned with the axis going through the center of the corner angle.  But he would get just 1.7 times the angular moment of one CD instead of the 3 times if he had stacked them all together.

By the way, somewhere there must be video of the demonstrations Nasa did with tops and described in this book:

(http://www.ta0.com/papyrus/images/Sumners.jpg)

From the Papyrus (http://www.ta0.com/papyrus/papyrus.html) section: "Nasa´s Toys in Space program flew several tops in two Shuttle flights. The tops included a pump top, a tippy top, a rattleback, gravitrons and gyroscope. Other spinning toys included a yo-yo and a magnetic wheel. "
Title: Re: Gyros & Tops in space
Post by: ta0 on October 17, 2013, 11:33:00 PM
Found the video showing the experiments with the Gravitron (an enclosed gyro top) by astronaut McMonagle on the Endeavour (ST-54.) The same experiment with three gyros is done but this time the (dubbed) explanation is correct, what is not surprising as the effect is much more obvious, explosive actually!  >:D

NASA - Toys in Space - Gravitron (http://www.youtube.com/watch?v=5cHIa8vhvTI#)
Title: Pioneer = Trompo
Post by: Ketzaltlipoka on October 19, 2013, 07:16:21 PM
Many, many years ago, I saw on tv a documental about Space exploration and there they showed the drawing that was sent to space, giving information about Earth and mankind.
In that then, I was not affected by this sickness of relationing Trompos with everything. But in that then I was already playing with trompos.
In the drawing appears something ( that according with this text,
http://en.wikipedia.org/wiki/Pioneer_plaque (http://en.wikipedia.org/wiki/Pioneer_plaque)
it seems to be the Pioneer) that in the first time I saw it, I clearly said to myself:
"that´s got the form of a trompo".

(http://upload.wikimedia.org/wikipedia/commons/thumb/0/02/Pioneer_plaque.svg/763px-Pioneer_plaque.svg.png)

Title: Re: Gyros & Tops in space
Post by: cecil on January 08, 2014, 01:23:24 AM
Over hand fighting. I love it.
Title: Toys In SPACE
Post by: johnm on February 10, 2014, 07:37:21 PM
many more fun "toys in space" videos on youtube now.

International Toys in Space: Spinning Top (http://www.youtube.com/watch?v=vedP40v0eDY#ws)

Yo-Yo Classics: Toys in Space (http://www.youtube.com/watch?v=mxzR7QW7BfM#)

A 23 minute movie of the Toys in Space program here:  STAR FLIX - TOYS IN SPACE: Just for FUN (http://www.youtube.com/watch?v=OPYjsa_JwcY#)
Title: Re: Gyros & Tops in space
Post by: ta0 on February 11, 2014, 11:18:22 AM
I agree with you Cecil, it looks like the man just threw a little top on the ground. When aliens find the Pioneer plaque they may well think it is a description of a spinning top game (played in the nude)   :P

On the first video I was surprised (as was the astronaut) that the top did not have more wobble when she added the weights to the rim.  I think the reason is that the stem has very little mass, so the new proper axis of rotation is still perpendicular to the disc and parallel to the stem. It would have shifted away from the center, but as the stem stays parallel to itself and does not describe a cone the wobble would not be very noticeable.  By the way, a top in micro-gravity will not do the normal precession, which is due to the pull of gravity.  But it can still do a precession-like movement if it is started spinning in a direction that does not coincide with a proper (principal) axis of rotation.
Title: Re: Gyros & Tops in space
Post by: Larry D. on February 11, 2014, 03:55:10 PM
Love the action with those Gravitrons!  :)
 
$9 buck including a holder, not bad.  Anyone know the cost of a Space Flight these days?
Title: Re: Gyros & Tops in space
Post by: Kirk on February 12, 2014, 07:12:04 PM
Anyone know the cost of a Space Flight these days?
All seats to fly to space are US$250,000 and deposits are refundable.
http://www.virgingalactic.com/booking/ (http://www.virgingalactic.com/booking/)
So far over 600 have been sold.
Title: space is fun
Post by: Daveid on August 22, 2015, 06:00:49 AM
http://sploid.gizmodo.com/space-makes-things-that-are-spinning-act-completely-cra-1725334216

https://www.youtube.com/watch?v=1n-HMSCDYtM
Title: Re: space is fun
Post by: the Earl of Whirl on August 22, 2015, 07:56:20 AM
Very interesting!!!
Title: Re: space is fun
Post by: ta0 on August 24, 2015, 01:23:50 AM
Very interesting indeed, and I would say related to spintop science so I am moving it out of NSTR  :)

This video is pretty amazing. It gives the impression of the handle flipping between two different stable spinning directions (bi-stable), what is not the usual description for this type of rotations.

Notice that with respect to the space station the rotation is always in the same direction (counter-clockwise looking towards the panel), as conservation of momentum requires. But from the T-handle's point of view (e.g., looking from the handles down to the key) the direction flips from counter-clockwise to clockwise.

Because the T-handle is symmetrical, the initial rotation must correspond to one of the principal axis of inertia. But it is unstable, so it has to be the one with intermediate amount of inertia as the other two axes are stable. This surprised me at first, but after thinking about it I realized that because the handles are more massive than the key shaft this is possible. I think the principal axis of maximum inertia must be perpendicular to the handles (and the shaft); the principal axis with minimum inertia must be in the plane of the handles (and perpendicular to the shaft). And I think the center of mass has to be pretty close to the handles for the other axis to be intermediate.
Title: Re: space is fun
Post by: dazzlingdave on August 28, 2015, 04:49:38 PM
The rotation switch is so cool!

That seems to be the same principle of the tippy top that when it flips it changes directions.

Speaking of that, I have been meaning to make a tippy top on my lathe......Maybe I should get to work!

Dave
Title: Re: space is fun
Post by: ta0 on August 28, 2015, 10:45:37 PM
The rotation switch is so cool!
That seems to be the same principle of the tippy top that when it flips it changes directions.
It is super cool and surprising, indeed!

The common explanation with the tippy top is that the friction from the table gives it the torque to flip. But perhaps you are right and some of this effect is helping the tippy top start the flip.

After thinking for a while about the video I have a tentative semi-intuitive explanation.
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.

Title: Tops in Space
Post by: cecil on October 18, 2016, 05:52:10 PM
https://youtu.be/Df-Jhnemhes

Me and Rosie got to try space.
Title: Re: Gyros & Tops in space
Post by: ta0 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!  ???
Title: Re: Gyros & Tops in space
Post by: Russpin 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 (https://www.youtube.com/watch?v=-2cMmwIKTJM)
Title: Re: Gyros & Tops in space
Post by: ta0 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:

(http://www.ta0.com/Button-n-String/Philippe_3axes.jpg)

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
Title: Re: Gyros & Tops in space
Post by: Russpin 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.
Title: Re: Gyros & Tops in space
Post by: ta0 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 (http://www.ta0.com/forum/index.php/topic,3051.msg40906.html#msg40906)!  :o

Title: Re: Gyros & Tops in space
Post by: Russpin 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 (https://www.youtube.com/watch?v=-2cMmwIKTJM)
Title: Re: Gyros & Tops in space
Post by: ta0 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.  ;)
Title: Re: Gyros & Tops in space
Post by: Russpin 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.
Title: Re: Gyros & Tops in space
Post by: Russpin 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 (https://www.youtube.com/watch?v=KkEN9T0YUCY)
Title: Re: Gyros & Tops in space
Post by: ta0 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.
Title: Re: Gyros & Tops in space
Post by: Jeremy McCreary on October 26, 2016, 10:02:23 AM
Very impressive simulations, Russpin! What programming language or software do you use?
Title: Re: Gyros & Tops in space
Post by: Russpin 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.
Title: Spinning T-handle in zero-g
Post by: Renee on July 07, 2019, 01:36:40 PM
https://youtu.be/1n-HMSCDYtM
Title: Re: Spinning T-handle in zero-g
Post by: Jeremy McCreary 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 (https://rotations.berkeley.edu/a-tumbling-t-handle-in-space)
Title: Re: Gyros & Tops in space
Post by: ta0 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 . . .
Title: Re: Gyros & Tops in space
Post by: Jeremy McCreary 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?

Title: Re: Gyros & Tops in space
Post by: Iacopo 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 !
Title: Re: Gyros & Tops in space
Post by: Jeremy McCreary 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.
Title: Re: Gyros & Tops in space
Post by: ta0 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.
Title: Re: Gyros & Tops in space
Post by: Iacopo 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.
Title: Re: Gyros & Tops in space
Post by: Jeremy McCreary 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.
Title: Re: Gyros & Tops in space
Post by: ta0 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.
Title: Re: Gyros & Tops in space
Post by: Jeremy McCreary 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.
Title: Re: Gyros & Tops in space
Post by: Jeremy McCreary on September 19, 2019, 08:04:57 PM
Just out on Veritasium -- a (kind of) intuitive explanation of the T-handle's flipping behavior...

https://youtu.be/1VPfZ_XzisU

In the process, the video gets into Explorer I"s brush with dissipation-induced instability. It also explains why the flipping behavior is variously called the "tennis racket theorem", the "intermediate axis theorem", or the "Dzhanibekov effect" -- the last after the Russian cosmonaut who first observed it in wing nuts in a microgravity setting.
Title: Re: Gyros & Tops in space
Post by: ta0 on September 19, 2019, 11:57:07 PM
Wow! Veritasium covers the subject pretty thoroughly. Nice!  8)

I do have a quip about the animation. It shows the little masses continuing to rotate in the same direction with respect to the large masses for the second period. I believe they should reverse direction, and the direction should oscillate back and forth (in this relative frame of motion). The way I think about it, if m1 starts a little above the y axis, it will finish a little above the (-)y axis on the other side, not at 180 degrees.

Although the explanation is not completely dissimilar to mine above, I think I now have a better intuitive idea of what is happening. I just read the original explanation by Terry Tao (link (https://mathoverflow.net/questions/81960/the-dzhanibekov-effect-an-exercise-in-mechanics-or-fiction-explain-mathemat)) and he also explains why this effect doesn't happen when you switch the axes (masses): Coriolis force dominates.

Veritasium seems to be very interested in rotating things. He must have seen some youtube videos with top tricking (perhaps the Figaro one with 1.6 million views.) I wonder if he has lurked on this forum.   ;) Think about it, perhaps even the other Tao has too . . .  :o  ;D ;D ;D
Title: Re: Gyros & Tops in space
Post by: Pepe on September 20, 2019, 09:11:22 AM
I need to go to space to do this thing!!!!

https://www.youtube.com/watch?v=1n-HMSCDYtM
Title: Re: Gyros & Tops in space
Post by: Jeremy McCreary on September 21, 2019, 01:40:45 AM
I do have a quip about the animation. It shows the little masses continuing to rotate in the same direction with respect to the large masses for the second period. I believe they should reverse direction, and the direction should oscillate back and forth (in this relative frame of motion). The way I think about it, if m1 starts a little above the y axis, it will finish a little above the (-)y axis on the other side, not at 180 degrees.

A difficult question.

I just read the original explanation by Terry Tao (link (https://mathoverflow.net/questions/81960/the-dzhanibekov-effect-an-exercise-in-mechanics-or-fiction-explain-mathemat)) and he also explains why this effect doesn't happen when you switch the axes (masses): Coriolis force dominates.

Thanks for the link. I get his Coriolis argument when the system rotates about the intermediate axis (through the smaller point masses on the rim of the disk). But not sure I follow when the rotation is about the axis axis through the larger masses.

Veritasium seems to be very interested in rotating things. He must have seen some youtube videos with top tricking...

Just in case, perhaps you should invite Derek to analyze some of your tricks.
Title: Re: Gyros & Tops in space
Post by: Iacopo on September 21, 2019, 08:13:26 AM
I do have a quip about the animation. It shows the little masses continuing to rotate in the same direction with respect to the large masses for the second period. I believe they should reverse direction, and the direction should oscillate back and forth (in this relative frame of motion).

In the last part of the video posted by Pepe it can be seen the motion from live at a lower speed.
In some way it remainds me of the tippe top, which flips over but without changing the direction of spinning.

I tried to read the Terry Tao explanation but I couldn't understand the reasoning about the Coriolis force.
It's a bit too out of reach for me..
 
Title: Re: Gyros & Tops in space
Post by: ta0 on September 21, 2019, 01:52:52 PM
But not sure I follow when the rotation is about the axis axis through the larger masses.
I tried to read the Terry Tao explanation but I couldn't understand the reasoning about the Coriolis force.
Actually, I don't think Tao fully explains why the Coriolis force is in the right direction and magnitude to neutralize the centrifugal effect. He just shows that it's there and will change the axis of rotation in the second case.

I do have a quip about the animation. It shows the little masses continuing to rotate in the same direction with respect to the large masses for the second period. I believe they should reverse direction, and the direction should oscillate back and forth (in this relative frame of motion). The way I think about it, if m1 starts a little above the y axis, it will finish a little above the (-)y axis on the other side, not at 180 degrees.
A difficult question.
In Tao's explanation, the force (and therefore acceleration) on the small mass is proportional to it's distance to the y axis. It's accelerated until it reaches the z axis and decelerated after that. So it should have zero speed when it reaches it's initial high over the y axis on the other side. From there it should reverse directions. Like a ball oscillating in the valley between two peaks.
Title: Re: Gyros & Tops in space
Post by: Iacopo on September 21, 2019, 04:28:15 PM
I do have a quip about the animation. It shows the little masses continuing to rotate in the same direction with respect to the large masses for the second period. I believe they should reverse direction, and the direction should oscillate back and forth (in this relative frame of motion). The way I think about it, if m1 starts a little above the y axis, it will finish a little above the (-)y axis on the other side, not at 180 degrees.
A difficult question.
In Tao's explanation, the force (and therefore acceleration) on the small mass is proportional to it's distance to the y axis. It's accelerated until it reaches the z axis and decelerated after that. So it should have zero speed when it reaches it's initial high over the y axis on the other side. From there it should reverse directions. Like a ball oscillating in the valley between two peaks.

Sorry, Ta0, I didn't understand.  You mean at 9:24, when the plate continues tilting in the same direction instead of tilting back.
I believe you are right, it seems like an inaccuracy in the animation.