- #1

- 1,170

- 3

## Main Question or Discussion Point

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?

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?