Use the 3-1-3 Euler angles to construct the rotation matrix Q as a succession of three rotations: a rotation by an angle o about the e3-axis, a rotation by an angle 0 about the b-axis, then a rotation by an angle y about the by-axis: {e;}i=1,2,3 qa() {b}}i=1,2,3 {b}}i=1,2,3 21(0) {b} }i=1,2,3 Pa (4) {bi}i=1,2,3 (i) Compute the resulting rotation matrix Q=Q3(0)Q1(0)23(4) and explain its geometric meaning, i.e., does it map vectors from body frame {b;}, where i 1, 2, 3, or vice versa? (ii) Does it admit any singularities? i.c., are there any angles 4, 0 or for which the matrix [C3, b, b) does not span the space? (iii) Compute the angular velocity matrix 120 QT, and the angular velocity matrix Ne = QQT which one corresponds to rotations from inertial frame to body frame and which one corresponds to rotations from body frame to inertial frame? (iv) What is the angular velocity vector w in body frame? in inertial frame? Use the 3-1-3 Euler angles to construct the rotation matrix Q as a succession of three rotations: a rotation by an angle o about the e3-axis, a rotation by an angle 0 about the b-axis, then a rotation by an angle y about the by-axis: {e;}i=1,2,3 qa() {b}}i=1,2,3 {b}}i=1,2,3 21(0) {b} }i=1,2,3 Pa (4) {bi}i=1,2,3 (i) Compute the resulting rotation matrix Q=Q3(0)Q1(0)23(4) and explain its geometric meaning, i.e., does it map vectors from body frame {b;}, where i 1, 2, 3, or vice versa? (ii) Does it admit any singularities? i.c., are there any angles 4, 0 or for which the matrix [C3, b, b) does not span the space? (iii) Compute the angular velocity matrix 120 QT, and the angular velocity matrix Ne = QQT which one corresponds to rotations from inertial frame to body frame and which one corresponds to rotations from body frame to inertial frame? (iv) What is the angular velocity vector w in body frame? in inertial frame