Q$1.$ Starting from $n^{}=Wn+Dn-(Dn*n)n$ where, $n$ is the unit vector in the direction of the

deformed material filament originally in the direction $N.$ Show that:

a$)$ Show that the rate of shear between two filaments is given by :

$-sin(){}^{}=2D{n}_1*n_2+(n_1*n_2)(-D{n}_1*n_1-D{n}_1*n_1)$

b$)$ Hence conclude that the off$-$diagonal components of $D$ capture the rate of shear.

c$)$ Also, from this show that filaments along the eigenvector directions of $D$ rotate

rigidly.