A Jacobian matrix and two equlibria are given. Determine if each is locally stable, unstable, or if the analysis is inconclusive. J=[ 2 x1 -sin x2 cos x1 0] (i) x̂1=1, x̂2=-π(ii) x̂1=1, x̂2=π | Numerade

3. Determine the Jacobian matrix [J] and its determinant for the elements shown in the figure below. Show that the determinant of [J] for rectangular and parallelogram shaped elements is equal to A=4, where A is the physical area of the element.