Statics via Lagrangians

least_action

Is it possible to do statics using lagrangians? (specifically building up a compound shape like a bridge from constrained point masses). Where could I see an example of this?

fobos3

Yes, just put the Lagrangian equal to the potential energy. However I think you will find that, if you have an equilibrium the potential energy is at minimum more useful. For example consider the cantenary.

[tex]V=\int_C my\,ds[/tex]

Now if you use Lagrangian mechanics you would be minimising [tex]\iint_C my\,ds\,dt[/tex] instead of [tex]\int_C my\,ds[/tex]

least_action

Thank you!