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Dzhanibekov effect or tennis racket theorem

Animation showing movement of a rigid body according to Dzhanibekov effect or tennis racket theorem

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DOWNLOAD-DESKTOP...nb
POSTED BY: Mariusz Iwaniuk
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Finally I have a tentative version of the demonstration based on explicit solution

Dzhanibekov Effect: http://arkadiusz-jadczyk.eu/docs/janiwdp2.nb

Excerpt on youtube: https://www.youtube.com/watch?v=ye-ONo-RixA

Would appreciate comments and suggestions how to improve.

UPDATE

The demonstration was published:

https://demonstrations.wolfram.com/DzhanibekovEffect
POSTED BY: Arkadiusz Jadczyk

enter image description here - another post of yours has been selected for the Staff Picks group, congratulations !

We are happy to see you at the top of the "Featured Contributor" board. Thank you for your wonderful contributions, and please keep them coming!
POSTED BY: EDITORIAL BOARD

Very cool. I was trying to recall the name of that effect for some time now. Here's another nice video of it in space: https://www.youtube.com/watch?v=BGRWg4aV2mw
POSTED BY: Paul Frischknecht
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POSTED BY: Arkadiusz Jadczyk

This is really nice, @Arkadiusz Jadczyk! One demonstration already came out of this:

The Intermediate Axis Theorem Applied to a Ping-Pong Paddle Flip-Over

but I think your should try sending this to Demonstrations team to see if they consider it different enough to publish.
POSTED BY: Vitaliy Kaurov

This demonstration now mentions this discussion:

Based on work by Mariusz Iwaniuk found at Dzhanibekov Effect or tennis racket theorem
POSTED BY: Vitaliy Kaurov

Privet Vitaliy, I am going to change my demonstration using explicit solution formula with Jacobi elliptic functions nad quaternions. That may be new.
POSTED BY: Arkadiusz Jadczyk

Very interesting. Did you find those with Mathematica or have some source like an article?

POSTED BY: Vitaliy Kaurov

One good article is by Cushman, "No polar coordinates"[1] https://www.maths.manchester.ac.uk/~jm/MASESS1/cushman.pdf
POSTED BY: Arkadiusz Jadczyk
POSTED BY: Arkadiusz Jadczyk

Yes, a little messed up moments of inertia, but corrected the "code". I also did simulations in Blender 3D. The results are similar, so as correct. :)

Ps: Change the file extension "Tennis Racet.nb" to "Tennis Racet.blend" . To run the simulation in Blender 3D, press on the keyboard "Alt + A".
POSTED BY: Mariusz Iwaniuk

In the original model ihave changed the values Ix,Iy,Iz to realistic

  Ix = 5.666666666666667`;
   Iy = 33.666666666666664`;
   Iz = 38.666666666666664`;

Then there is a strange phenomenon - After restart colors Green and Blue change a while before the flip, like in precognition. I do not understand what is the reason? I am not sure if this effect is reproducible.
POSTED BY: Arkadiusz Jadczyk

This strange phenomenon is associated only with animation,because is looped .

enter image description here
POSTED BY: Mariusz Iwaniuk
Erik Mahieu
Erik Mahieu
Posted 11 years ago

Hello Mariusz I looked at your code and at the moments of inertia in your example... It is because in your specific case, the intermediate axis (due to the geometry and position of the centroid) the intermediate axis is the one parallel with the blade (the psi axis). And it does not give such a nice and smooth ride?? enter image description here

The angular speed plot on the left is from the paddle in my previous reply, the plot to the right is from your paddle You can see that in my case, the unstable rotation is around the theta axis (yellow curve), whereas in your case, the unstable rotation is around the psi axis (green curve) BTW, it is not recommended to use subscripted variables in Mathematica code. It sometimes gives problems. Thanks for yr interest in this case!
POSTED BY: Erik Mahieu
Erik Mahieu
Erik Mahieu
Posted 11 years ago

I am aware of this video and indeed, the axis parallel to the paddle blade could also be an intermediate axis for some geometries or materials used in the paddle. In my example, I consider the paddle to be made of homogenous material of density 1 and with arbitrary dimensions that may not be realistic compared to real world ping pong equipment. In my example, the axes are crossing at the centroid: the intermediate axis is the phi axis perpendicular to the blade; in the video example it is more than likely the psi axis, parallel to the blade? Both are possible depending on the location of the centroid ( geometry, density distribution, etc...) You can see that the the two largest moments are very close compared to the minimum moment of inertia.enter image description here
POSTED BY: Erik Mahieu

I solved the problem. Animation is a solution of 6 equations.

enter image description here

POSTED BY: Mariusz Iwaniuk
Erik Mahieu
Erik Mahieu
Posted 11 years ago

Hello, Mariusz, I am working on a Wolfram Demonstrations based on your idea and the suggestion from Sam Carrettie. I am using a ping pong paddle to demonstrate the "Intermediate Axis Theorem" of which the Dzhanibekov Effect is another example. I am still working out the details but attached is a *.mov file to show the output. Thanks for you post.

/Users/erikmahieu/Downloads/paddle.tiff

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POSTED BY: Erik Mahieu
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POSTED BY: Mariusz Iwaniuk
POSTED BY: Mariusz Iwaniuk

This is great, thanks for sharing! This can make a nice Demonstration. I am curious if this is also easy in SystemModeler.
POSTED BY: Sam Carrettie
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