NYC physics and math self-learners group Message Board › Today's meeting
New York, NY
We had a successful first meeting of 2013. I'm not posting a photos of it only because I don't want those who couldn't make it to feel too bad on observing the general euphoria. (Also, I didn't take any.) From now on, we'll meet on THE FIRST SUNDAY OF EVERY MONTH, AT 4 PM. Please block it out on your calendars (now). I will announce the next meeting soon.
Today's meeting was pretty well-attended. Tarun, who had been planning to lead the discussion, couldn't make it because he was sick. So we muddled though a derivation of the Euler/Lagrange Equations on our own. If you want to work ahead in the coming month, keep doing the theory and the odd-numbered problems (working upward from problem 1) in chapter 2 of Classical Mechanics (2nd ed.) by Herbert Goldstein. As I mentioned today, Goldstein is such a common textbook there are likely to be solutions to many of his problems on line. For example, here's one attempt at solutions to the 2nd edition: http://homerreid.ath..... If you have questions or thoughts about anything you read in Goldstein, please post them on the Meetup site, under the discussion thread for our upcoming meeting (as soon as I create one). People can respond on line, or save their answers for the next meeting.
Apropos of today's meeting, here is a discussion of the "proof by picture" of how you minimize/maximize a scalar function of position and velocity over all possible paths -- i.e., a pictorial derivation of the Euler/Lagrange Equations: http://www.physicsins.... I recommend skipping to the part that says "A Second Derivation: A Bit Less Clear, but More Correct." It's plenty clear.
Also, at the end of today's meeting, I was mentioning that the Hamiltonian formulation is just a Legendre transform of the Euler-Lagrange Equations. To get the intuition for what a Legendre transform is, there are plenty of good sources on line. Here are a few that look useful:
Some of the above sources were circulated in prior months by others in the group. I just wanted to re-circulate them for the benefit of the newer folks. I'll be in touch soon.