Problem 1 (Spatial Description) [6 marks]\ A body frame

{B}

is initially coincident with the reference frame

{R}

. The final orientation of frame

(

{

B}

) is determined by the following three rotations; rotate

{B}

about

x_(R)

by 30 degrees, rotate

(B)

about

Z_(R)

by 45 degrees, and finally rotate (B) about

Y_(R)

by 60 degrees.\ i) [3 marks] Express

R_(B)^(R)

in terms of elementary tolation matrices.\ ii) [3 marks] If the second rotation is about

Z_(n)

by 45 degrees, express

R_(B)^(R)

in terms of elementary rotation matrices.\ Solution

A body frame {B} is initially coincident with the reference frame {R}. The final orientation of frame (B} is determined by the following three rotations; rotate {B} about XR by 30 degrees, rotate (B} about ZR by 45 degrees, and finally rotate {B ) about YR by 60 degrees. i) [3 marks] Express RBR in terms of elementary rotation malrices. ii)[3 marks] If the second rotation is about Z Zy by 45 degrees, express RBR in terms of elementary rotation matrices