5 ms·
"IMHO, neither of these other developments is as intuitive as the Lagrange multipler one; but because Hamilton's original formulation obscures it, no one in phy
by starwed 16y ago
"IMHO, neither of these other developments is as intuitive as the Lagrange multipler one; but because Hamilton's original formulation obscures it, no one in physics learns it that way."
I'm pretty sure learning a bit about Lagrange multipliers is standard for a grad classical mechanics class. Granted, I've forgotten all I learned back then, b/c it has never come up in anything else I do, but it was definitely part of the course.
- ArbitraryLimits 16y agoI believe it used to be standard to use Lagrange multipliers to handle constraints on the state space in R^n as an alternative to using generalized coordinates. For example, when you handle the case of motion on the surface of a sphere you can either use R^3 with a Lagrange multiplier enforcing the constraint that you stay on the surface of the sphere, or you could use latitude/longitude as coordinates. The interpretation of the momenta themselves as Lagrange multipliers is completely nonstandard, though. Try googling "hamiltonian mechanics lagrange multipliers"; you'll get either examples like the sphere thing or hits from optimal control tutorials.