The discussion confirms that Lagrangian mechanics can be applied to statics, particularly in constructing compound shapes like bridges from constrained point masses. The key approach involves equating the Lagrangian to the potential energy, with an emphasis on minimizing potential energy for equilibrium scenarios. The catenary is highlighted as a relevant example, where the potential energy is expressed as V = ∫C my ds, and the Lagrangian mechanics formulation involves minimizing the expression ∫∫C my ds dt.
PREREQUISITESStudents and professionals in physics and engineering, particularly those focusing on mechanics, structural analysis, and optimization techniques in statics.
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?
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