Elasticity/Sample quiz 3

Given the displacement vector
 * $$     \mathbf{u} = X_1^2 X_2 \widehat{\mathbf{e}}_{1} + X_3 \widehat{\mathbf{e}}_{2} + X_3^2 \widehat{\mathbf{e}}_{3}

$$
 * 1) Find the strain tensor $$\boldsymbol{\varepsilon}$$ and the rotation tensor $$\mathbf{W}\,$$.
 * 2) Write down the compatibility equation in the $$\widehat{\mathbf{e}}_{1}$$- $$\widehat{\mathbf{e}}_{2}$$ plane. Use index notation with commas representing partial derivatives with respect to Lagrangian material co-orinates.