Which systems satisfy Hamiltons principle

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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?
 

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Simon Bridge
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Are all the fundamental forces observed in nature in a form like this? And is that then the deep content in Hamiltons principle?
Yes and yes. That would be my understanding too.

Text books are trying to account for different learning styles so they sometimes try too hard.
 

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