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In Cushman and Bates, Global Aspects of Classical Integrable Systems, 1997, I have read

In a widely circulated but unpublished letter in 1965, Palais explained the symplectic formulation of Hamiltonian mechanics.

I would like to know if, in the meanwhile, this letter was made available.

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2 Answers 2

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I haven't thought about that letter for a very long time, but as far as I can recall I didn't ever make it publicly available, and I don't think any of the friends to whom I sent it did either. However, I am a bit of a pack-rat, so after Ryan Budney alerted me that this question had appeared on MO I did some searching in my piles of old papers, and I found and scanned what I am pretty sure was the mathematical content of the letter, and here is a link to the scan.

http://vmm.math.uci.edu/PalaisLetterOnSymplectic.pdf

(I'm not sure if I just sent out copies of this with a cover letter or rather wrote a letter in which I copied the contents of the above.)

Note, that the first page of the above is a scan of page 159 of "Foundations of Mechanics" by Ralph Abraham and Jerry Marsden. It says that the letter was from around 1962, which is what I recall. Ralph was one of the recipients. Dick Palais

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    $\begingroup$ The answer to the question is, therefore, apparently no :-) $\endgroup$
    – Mariano Suárez-Álvarez
    Commented Aug 15, 2012 at 18:24
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    $\begingroup$ @Mariano: Yes, I guess that was a pretty verbose "no". :-) Dick $\endgroup$
    – Dick Palais
    Commented Aug 15, 2012 at 18:35
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    $\begingroup$ Dear Professor Palais I am very grateful to you. Sincerely I was afraid that without having been published in fifty years it had now gone missing, and that would be a loss. Initially I thought the network formed by MO-users around the world as the best tool to gather informations about the history of the letter from its origin until now.. Only if this were not enough then we could contact you. But, somehow, there was no need. Thank you. I'm really glad that this your letter has come so far, and will thus be able to continue its journey. Thank you. $\endgroup$
    – agt
    Commented Aug 15, 2012 at 20:38
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    $\begingroup$ Fantastic use of MO. $\endgroup$
    – Deane Yang
    Commented Aug 15, 2012 at 20:52
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I would like to know if, in the meanwhile, this letter was made available

Yes! (See here).

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    $\begingroup$ This post made me chuckle. Thank you. $\endgroup$
    – G. Fougeron
    Commented May 28, 2021 at 13:00

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