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

AI Thread Summary
Using Lagrangians for statics is possible by equating the Lagrangian to potential energy, which can be particularly useful in analyzing equilibrium conditions. In cases like building a compound shape such as a bridge from constrained point masses, the potential energy approach often yields more straightforward results. The discussion highlights the catenary as a relevant example, emphasizing the importance of minimizing potential energy in equilibrium scenarios. The Lagrangian mechanics approach involves a more complex minimization process compared to traditional potential energy methods. Overall, understanding these principles can enhance the analysis of static structures.
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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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least_action said:
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
 
fobos3 said:
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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