- #1
Zeno Marx
- 18
- 0
Hi, I was wondering about the interpretation of the Hamilton Jaccobi equation.
Naively we have H + [itex]\partial[/itex]S/[itex]\partial[/itex]t = 0 where H is the Hamiltonian and S is the action. But the action is the time integral of the Lagrangian so you would expect [itex]\partial[/itex]S/[itex]\partial[/itex]t = L
Thus H + L = KE + PE + KE - PE = 2KE = 0
(PE = potential energy, KE = Kinetic energy)
Which simply says that then system is not moving which seems odd for something billed as an equation of motion. Something is clearly very wrong here but what?
Naively we have H + [itex]\partial[/itex]S/[itex]\partial[/itex]t = 0 where H is the Hamiltonian and S is the action. But the action is the time integral of the Lagrangian so you would expect [itex]\partial[/itex]S/[itex]\partial[/itex]t = L
Thus H + L = KE + PE + KE - PE = 2KE = 0
(PE = potential energy, KE = Kinetic energy)
Which simply says that then system is not moving which seems odd for something billed as an equation of motion. Something is clearly very wrong here but what?