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Hello, could You, please, add that this effect was observed and recorded in space before Dzhanibekov - during Apollo 11 mission in 1969? I noticed it watching Apollo 11 (2019) movie using only source materials: Neil Armstrong puts hard drive disc into rotating state and disc flips over around 1st and 3rd principal axis few times. I think it is worth to mention. Thanks. ( youtube video of this moment: /cOhqC6FpjOk ) — Preceding unsigned comment added by 83.9.145.146 (talk) 09:21, 16 April 2023 (UTC)
Is it possible to analyse this theorem quantitatively? Like finding out how much flipping takes place in what time and all? Roshan220195 (talk) 08:07, 25 March 2012 (UTC)
A broken link in the cite "Mark S. Ashbaugh, Carmen C. Chicone and Richard H. Cushman, The Twisting Tennis Racket, Journal of Dynamics and Differential Equations, Volume 3, Number 1, 67-85 (1991)" Jdeliagtm (talk) 14:38, 19 October 2014 (UTC)
There is no such theorem. There Euler's theorem. She was 200 years old.84.250.10.131 (talk) 22:13, 16 December 2014 (UTC)
The twisting tennis racket theorem is much more than just the instability of the intermediate axis. The latter has been known for a long time, while the tennis racket theorem was proved in the Ashbaugh, Chicone, Cushman paper of 1989. It analyses the Hamiltonian system on T*SO(3) corresponding to a rigid body rotating around the intermediate axis by taking the symplectic reduction by the symmetry around the long axis. The reduced system has two hyperbolic fixed points. When the racket is thrown, the system oscillates between the two points, spending most of its time near the hyperbolic points while moving quickly from one to the other. This corresponds physically to the system executing precise 180 degree twists repeatedly, as illustrated by the famous "dancing t-handle" video from the Russian space station. I intend to edit the page and add roughly this statement while fixing the citation. MatthewCushman (talk) 01:34, 2 February 2018 (UTC)
The intermediate axis theorem is not the tennis racket theorem (as explained in the above comment) so I believe that should be made clear. I would mention the precise distinction. I intent to change this in the first paragraph and add a second going into detail on the actual theorem. MatthewCushman (talk) 08:11, 2 February 2018 (UTC)
The article describes what happens but not why it happens. Why is angular momentum about each axis not conserved? Why is a rigid object that's free of outside forces behaving in a non-linear way? What's the source of the instability?
An equation describing what happens is not an explanation of the underlying mechanics. Michael McGinnis (talk) 18:36, 18 June 2018 (UTC)
I have removed the following sentence from the article:
An article explaining the effect was published in 1991.[1]
References
Possibly the reference could be used so source some content in the article, but the sentence is of no encyclopedic value and certainly doesn't belong in the lead section. --JBL (talk) 23:31, 19 December 2019 (UTC)
Dear All, I found that Dzhanibekov effect was recorded during Apollo 11 mission in 1969. I think it is worth mentioning. You can find reference in Apollo 11 movie from 2019 where there is original footage of this phenomena. Original Time: 1:16:08 - 1:16:14. Available also on Youtube under watch?v=cOhqC6FpjOk — Preceding unsigned comment added by 178.42.19.59 (talk) 20:16, 6 February 2020 (UTC)
The following discussion is copied from my talk page, with permission. In concerns this edit. --JBL (talk) 13:29, 17 February 2020 (UTC)
You reverted my edit to https://en.wikipedia.org/wiki/Tennis_racket_theorem I do not understand why we need a secondary source to show that someone knew the theorem 150 years ago... the primary source clearly shows that someone knew the theorem that far back. What kind of secondary source are you looking for? AristosM (talk) 01:08, 16 February 2020 (UTC)
End copy. --JBL (talk) 13:29, 17 February 2020 (UTC)
The main text calls the handle axis the third axis, but in the picture this is the first axis. Conversely the main text call the vertical axis perpendicular to the the racket the first axis but in the picture this is the third axis. My intuition tells me that the picture is correct and the text is not but perhaps I got it upside down. In any case it seems that at least one of the two is wrong and it would be great if someone more knowledgeable than me could fix this. Octonion (talk) 15:25, 20 February 2020 (UTC)
Hi Octonion, I just noticed this too! Unfortunately, like you, I've no idea which is the true first and which is the true third. Also I can't wait til I get my hand on a tennis racket to try this theorem out. 2A02:C7D:DA5D:4F00:1104:AE91:F40B:DA65 (talk) 16:58, 23 May 2020 (UTC)
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The sign convention used for euler's equations is inconsistent with https://en.wikipedia.org/wiki/Euler%27s_equations_(rigid_body_dynamics). I believe there is a sign error
This is how it is listed on https://en.wikipedia.org/wiki/Tennis_racket_theorem I_{1}{\dot {\omega_{1}&=(I_{3}-I_{2})\omega _{3}\omega _{2} I_{2}{\dot {\omega ))_{2}&=(I_{1}-I_{3})\omega _{1}\omega _{3} I_{3}{\dot {\omega ))_{3}&=(I_{2}-I_{1})\omega _{2}\omega _{1}
According to https://en.wikipedia.org/wiki/Euler%27s_equations_(rigid_body_dynamics) It should be I_{1}{\dot {\omega ))_{1}&=(I_{2}-I_{3})\omega _{3}\omega _{2} I_{2}{\dot {\omega ))_{2}&=(I_{3}-I_{1})\omega _{1}\omega _{3} I_{3}{\dot {\omega ))_{3}&=(I_{1}-I_{2})\omega _{2}\omega _{1}
As a result there are sign errors in the rest of this page. 192.139.0.195 (talk) 23:02, 12 July 2022 (UTC)
The 4 th para implies this only applies to symmetrical objects - it applies to any object. The tensor of inertia is always symmetrical, and so can be rotated to a diagonal matrix with 3 principal axes and inertias. Dylanmenzies (talk) 13:06, 19 July 2023 (UTC)
Better to call "Matrix analysis" Dynamic Analysis, and "Geometric Analysis" Invariants analysis Dylanmenzies (talk) 13:17, 19 July 2023 (UTC)
minor point - the ellipsoids chosen are clearly not consistent or representative, because the constraints on the ratios os principal axes. Dylanmenzies (talk) 13:28, 19 July 2023 (UTC)