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

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!