Talk:Tennis racket theorem

Firstly observed in space during Apollo 11 mission
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)

Page TODOs
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 is no such theorem. There Euler's theorem. She was 200 years old.84.250.10.131 (talk) 22:13, 16 December 2014 (UTC)

I intend to make the following changes, what do others think?
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)

A physical explanation of the instability is needed
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)


 * There's a discussion of the physical principles behind this in this StackExchange thread in which Terence Tao gives some excellent insights. This video has a visualization of Tao's explanation. -- The Anome (talk) 11:11, 1 October 2019 (UTC)

Pointless sentence
I have removed the following sentence from the article: "An article explaining the effect was published in 1991."

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)

It was recorded before
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)

Poinsot
The following discussion is copied from [https://en.wikipedia.org/w/index.php?title=User_talk:Joel_B._Lewis&oldid=941250932#Why_do_we_need_a_secondary_source_for_what_the_text_actually_says? 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)


 * Hi, Thanks for your message. The relevant piece of policy is WP:PSTS.  Poinsot's paper is the document that exhibits the fact of someone in the 19th century knowing this theorem. A proper secondary source for the statement "it was known 150 years ago" would be someone commenting on the fact that Poinsot wrote a paper in the 19th century that contained this theorem; for example, a piece of literature on the history of physics, or a physics textbook by a reputable scholar published through a conventional editorial process.
 * To understand why this matters, consider whether our article on the four color theorem should state that it was proved by Kempe in 1879; certainly, I can find a primary source that says it was (namely, the one written by Kempe in 1879), but all modern secondary sources agree that the proof was flawed and so allow us to comment on the subject with appropriate perspective.
 * A secondary source would also be helpful for clarifying whether Poinsot's work is correctly dated to 1834 or 1852: you changed it from 1834 to 1852 based on the image (a primary source), but it's quite possible that this was a republished version of an earlier work, or that the result was first shared in personal correspondence earlier, or one of many other things that could make the earlier date correct. To be clear, I have no idea if this is the case; but a good secondary source would settle the question. --JBL (talk) 01:57, 16 February 2020 (UTC)
 * I see. That's a complicated piece of reasoning. Would the Veritaserum video count as such a secondary source? https://www.youtube.com/watch?v=1VPfZ_XzisU See timestamp 4:48 through 5:10, where he discusses explicitly that the theorem published earlier is the same as the current theory. AristosM (talk) 15:33, 16 February 2020 (UTC)
 * I think it is good (although it doesn't settle the question of the correct date); I will add it to the article. Thanks!  --JBL (talk) 16:33, 16 February 2020 (UTC)
 * The first printing was 1834: https://www.worldcat.org/title/theorie-nouvelle-de-la-rotation-des-corps/oclc/12744728 AristosM (talk) 19:22, 16 February 2020 (UTC)
 * The 1834 "edition" is a text only paper, which does not give derivation of any results. The 1851 edition contains the derivation of the result. The link in the references is to the 1851 edition. WorldCat claims that both were also immediately translated into English. 75.155.165.57 (talk) 20:44, 31 July 2023 (UTC)

End copy. --JBL (talk) 13:29, 17 February 2020 (UTC)

First, second and third axis in tennis racket
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)
 * ✅ Updated lede as per Reference_desk/Science.
 * I don't have access to http://link.springer.com/article/10.1007%2FBF01049489 but another paper uses the convention I1≤I2≤I3 whereas the article uses I1&gt;I2&gt;I3. I've fixed the lede by referring to the notation used in the image and am leaving the prose for someone else to amend if needed. Cheers, cm&#610;&#671;ee&#9094;&#964;a&#671;&#954; 23:42, 19 June 2021 (UTC) cm&#610;&#671;ee&#9094;&#964;a&#671;&#954; 23:22, 19 June 2021 (UTC)
 * Fixed prose as per http://en.wikipedia.org/w/index.php?title=Tennis_racket_theorem&diff=1030939977&oldid=1030291223 cm&#610;&#671;ee&#9094;&#964;a&#671;&#954; 21:54, 28 June 2021 (UTC)

Semi-protected edit request on 12 July 2022
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)
 * Red question icon with gradient background.svg Not done: it's not clear what changes you want to be made. Please mention the specific changes in a "change X to Y" format and provide a reliable source if appropriate. Aaron Liu (talk) 13:44, 13 July 2022 (UTC)
 * e.g. see this: https://thatsmaths.com/2019/12/12/the-intermediate-axis-theorem/ As stated in the previous comment, I also believe the sign should be changed according the already mentioned Euler's equations. — Preceding unsigned comment added by Ezorzin (talk • contribs)
 * I agree, and I have fixed the sign Kishore G (talk) 12:30, 11 May 2023 (UTC)

Scope of rigid objects
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)


 * Note also that the animation has no axis labels, so it is not clear what is being plotted. Since the Energy surface appears strongly to be a sphere, the axes must be \sqrt{I_i\omega_i}. If \omega_i were wanted, then the Energy surface should also be an ellipse. In any case, there should be a re-scaling factor (Eg (I_1 I_2 I_3)^{1/3}) since the energy and the angular momentum squared do not have the same dimension, so E=L^2 could occur at any value of omega depending on the units chosen. 75.155.165.57 (talk) 20:57, 31 July 2023 (UTC)

Headings
Better to call "Matrix analysis"  Dynamic Analysis, and "Geometric Analysis" Invariants analysis Dylanmenzies (talk) 13:17, 19 July 2023 (UTC)

Ellipsoid animation
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)