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Statics via Lagrangians

by least_action
Tags: lagrangians, statics
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least_action
#1
Jul22-10, 06:26 AM
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?
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fobos3
#2
Jul22-10, 06:47 PM
P: 35
Quote Quote by least_action View Post
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.

[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
#3
Jul23-10, 08:46 AM
P: 22
Quote Quote by fobos3 View Post
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]
Thank you!


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