I have had similar questions posted, but I am not quite sure on this one and it seems that my textbooks have trouble agreeing completely aswell. As far as I understand it: Hamiltons principle: δI = δ∫Ldt = 0 is only satisfied for systems, where the generalized forces can be put in a form such that the equation: d/dt([itex]\partial[/itex]L/[itex]\partial[/itex]q') - [itex]\partial[/itex]L/[itex]\partial[/itex]q = 0 is satisfied. I have seen that this can be done for electromagnetic systems and system in which the force can be written as the gradient of a potential with respect to the position coordinates. My question is: Are all the fundamental forces observed in nature in a form like this? And is that then the deep content in Hamiltons principle?