Q$1$

$6$ Points

Consider three frames, $F_0=o_0{x}_0{y}_0{z}_0,F_1=o_1{x}_1{y}_1{z}_1,$ and $F_2=o_2{x}_2{y}_2{z}_2.$ Frame $F_1$ is obtained from $F_0$ by a rotation of $R_1^0=$ exp$(S(a(t))).$ Frame $F_2$ is obtained from $F_1$ by a rotation of $R_2^1=$ exp$(S(b(t)))$

Q$1\mathrm{.}1$

$4$ Points

If $a(t)=[t,2t,3t{]}^{TT}$ and $b(t)=[2t^2,7t^2,8t^2{]}^{TT},$ what are the angular velocities corresponding to both rotation matrices $R_1^0$ and $R_2^1?$