Notes on Lagrangian continuum mechanics

Abstract

In Continuum Mechanic a simple material body $\mathcal{B}$ is represeted by a three-dimensional differentiable manifold and the configuration space is given by the space of embeddings $Emb\left(\mathcal{B},{\mathbb{R}}^n\right)$. We use the topology of infinite-dimensional manifold of this space, to present the first variation formula for Lagrangian mechanics.