Learn How to Use Lagrangians for Statics: Building Compound Shapes and Examples

[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]

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

 

[least_action]

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!