4 ms·

Okay, but what's the point? Yes, it's possible to write down the Hamiltonian and Lagrangian formulations in a form that high school kids can understand. To wh

Okay, but what's the point? Yes, it's possible to write down the Hamiltonian and Lagrangian formulations in a form that high school kids can understand. To what end? The reason these formulations are preferred is that certain classes of problems and generalizations become easy when you look at mechanics from these points of view, whereas in the "usual" setup there's no obvious way to proceed, but most of these problems are too difficult for high school kids to touch, and the utility of the abstractions will be lost on them altogether. They just become another set of equations to memorize, with no idea why anyone would write them that way... This is particularly true with the Lagrangian and Hamiltonian formulations - as presented, they are absolutely trivial rearrangements of the equations of motion. Their power only presents when you look at how they generalize to more complex situations. It always bothers me when people try to slip advanced material into lower level education without addressing the "why?" question. A shallow explanation backed by a few equations doesn't help anyone, and in the worst cases it can make the material seem even more obscure and mysterious.

kurtosis 18y ago
yeah this was a pretty lame introduction, but there are several BIG ideas in lagrangian and hamiltonian mechanics that I think would be entirely appropriate for HS - in fact the earlier people are exposed to these the better. (1) The local motion always "chooses" a path which optimizes a "global" property (the action). A system which follows only local rules can find a global optimum. This is a very important idea. I think this point finally made it into a nobel lecture for economics maybe 200+ years after maupertuis, d'alembert and of course, lagrange. (2) Knowledge of the conserved quantities completely determines the motion. Conservation laws take on their simplest form in the hamiltonian formulation. I was very fortunate to have a high school teacher who introduced me to these ideas then. It's probably the reason I decided to study physics!
- seanc 18y ago
  Well, yes, putting the sarcasm below aside, I agree that this is Really Cool Stuff. Reminds me of the bit in Anathem when Fraa Erasmas teaches Barb about Hilbert Spaces because, dammit, he was ready, and why make somebody go through the pain of doing it wrong when they're ready to learn how to do it the easy way?

kurtosis 18y ago

yeah this was a pretty lame introduction, but there are several BIG ideas in lagrangian and hamiltonian mechanics that I think would be entirely appropriate for HS - in fact the earlier people are exposed to these the better. (1) The local motion always "chooses" a path which optimizes a "global" property (the action). A system which follows only local rules can find a global optimum. This is a very important idea. I think this point finally made it into a nobel lecture for economics maybe 200+ years after maupertuis, d'alembert and of course, lagrange. (2) Knowledge of the conserved quantities completely determines the motion. Conservation laws take on their simplest form in the hamiltonian formulation. I was very fortunate to have a high school teacher who introduced me to these ideas then. It's probably the reason I decided to study physics!

seanc 18y ago
Well, yes, putting the sarcasm below aside, I agree that this is Really Cool Stuff. Reminds me of the bit in Anathem when Fraa Erasmas teaches Barb about Hilbert Spaces because, dammit, he was ready, and why make somebody go through the pain of doing it wrong when they're ready to learn how to do it the easy way?