Timeline for Inconsistency in Lagrangian vs Hamiltonian formalism?

7 events

when toggle format	what		by	license	comment
May 18, 2017 at 23:45	vote	accept	donnydm
May 18, 2017 at 13:21	answer	added	J.G.		timeline score: 7
May 18, 2017 at 13:11	comment	added	lalala		Try to calculate $p_\eta$ ist zero.So you cannot express the velocity in terms of the momenta. This is called a constraint system. Dirac wrote a small book how to deal with that (since Electrodynamics is also a constraint system this is relevant for physics)
May 18, 2017 at 13:10	history	edited	Qmechanic♦		edited tags
May 18, 2017 at 13:08	comment	added	JamalS		Off the top of my head, note that as you computed, $\frac{\partial L}{\partial \dot \eta} = 0$ and so $p_\eta = 0$. As such, $H$ cannot be written as some unique function of $p_\eta$ in any sense, and I don't think that $\frac{\partial H}{\partial p_\eta}$ would be well-defined.
May 18, 2017 at 13:08	comment	added	Qmechanic♦		Hints: 1. For starters, there is a primary constraint $p_{\eta}\approx 0$. 2. I discuss this example in my Phys.SE answer here.
May 18, 2017 at 13:01	history	asked	donnydm	CC BY-SA 3.0