Time: 4:00 pm
Location: LaunchPad (721 Franklin Ave., Brooklyn)Price: suggested donation
At the NYC Physics & Math Self-Learners, we basically work our way through graduate physics materials, and meet on the first Sunday afternoon of each month to discuss what we've learned and to answer one another's questions. The emphasis is on intuition rather than problem-solving methods, but we do both. We will do the following this month: 1. Prove, geometrically if possible, that the Legendre Transform is its own inverse. (Clement got us started last time, by suggesting that we consider a function that its just a bunch of little line segments joined at vertices. Prove the result for such a function, then take a smooth function to be a limiting case. Everyone please try to demonstrate the result rigorously, using this picture -- or any other intuitive pictures you can glean from the Internet or life.) 2. Quickly re-derive Hamilton's Equations and Liouville's Theorem (briefly, since we've done it before) 3. Go through Routh's Procedure (sec 8-3 in Goldstein 2nd ed.) in detail. Make sure we all get it. I think it may be important later 4. If time allows, derive Hamilton's Equations using a variational principle, as done in sec. 8-5 of Goldstein Anyone who wants to lead discussion of any of 1-4, inclusive, please let me know and I'll sign you up. I volunteer to do 2, since it is easy. I will try to volunteer for one more, once I'm convinced I can do it.
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