Recent content by Bosh

This has been my approach. I should have added that the additional terms are a perturbation, so I'm trying to achieve even just the simpler goal of matching terms to the next order in epsilon. Even so, I'm only close in a simple case, and in complicated cases it seems hopeless to get everything...

Imagine I have a complicated second-order differential equation that I strongly suspect can be derived from a Hamiltonian (with additional momentum dependence beyond p2/2m, so the momentum is not simply mv, but I don't know what it is). Are there any ways to test whether or not the given...

Hi Vanhees, sorry yes I've been reading all your posts carefully, I just have agreed with everything you said so I didn't comment on it. I am completely on the same page as you that the variational principle in the Hamiltonian formalism is more general than that in the Lagrangian. But I'm...

Hm, thanks for the reply Mr. Vodka. I'd be interested to see what other people think. I'm not sure that looking at the Lagrangian problem in q and \dot{q} space is quite right. I think the variation is done in q, t space, and when you derive the condition for the action to be minimized, since...

Mr. Vodka: If you look at how you derive the Euler-Lagrange equations in the Lagrangian formalism, you don't vary q and \dot{q} independently. What you do is you vary the path q(t), and that creates variations in q and \dot{q} that are related to each other through \delta \dot{q} =...

Right, I think where I'm getting confused is that with Lagrangians, along any path you can't vary q without varying \dot{q}. I therefore have trouble seeing how you can transform to a Hamiltonian and now vary q and p independently. p = \frac{\partial L}{\partial \dot{q}}, so since L = L(q...

Hi, A fundamental aspect in the Hamiltonian framework of mechanics is that the q's and p's are independent. I feel like I understand the steps in the Legendre transform from Lagrangian to Hamiltonian mechanics, but I don't see how you can go from a system where only the q's are independent...