Talk:Tennis racket theorem

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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)[reply]

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)[reply]

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)[reply]

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)[reply]

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)[reply]

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)[reply]

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