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.
(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