# Statics via Lagrangians

by least_action
Tags: lagrangians, statics
 P: 22 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?
P: 35
 Quote by 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?
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.

$$V=\int_C my\,ds$$

Now if you use Lagrangian mechanics you would be minimising $$\iint_C my\,ds\,dt$$ instead of $$\int_C my\,ds$$
P: 22
 Quote by 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. $$V=\int_C my\,ds$$ Now if you use Lagrangian mechanics you would be minimising $$\iint_C my\,ds\,dt$$ instead of $$\int_C my\,ds$$
Thank you!

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