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The first Piola-Kirchoff stress tensor and its corresponding Lagrangian can be used to model large deformations in elastic bodies. In the animation below, I simulated large deformations in four different tetrahedral meshes by calculating their PK1 stress tensors using FEM.
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Using the standard "F=ma" approach to model a double-rod pendulum is very demanding because we need a separate set of variables for each particle in the system. However, with Lagrangian mechanics, we can reduce the number of variables to just a couple degrees of freedom!
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