ME$/$ECE $5463$ Homework Set $1$

$2.($Exercise $3\mathrm{.}15,$ Lynch and Park$)$

$($a$)$ Given a fixed frame $\{0\}$ and a moving frame $\{1\}$ initially aligned with $\{0\},$ perform the following sequence of rotations on $\{1\}$ :

i$.$ Rotate $\{1\}$ about the $\{0\}$ frame vec$(x)-$axis by $$; call this new frame $\{2\}.$

ii$.$ Rotate $\{2\}$ about the $\{0\}$ frame vec$(y)-$axis by $$; call this new frame $\{3\}.$

iii. Rotate $\{3\}$ about the $\{0\}$ frame vec$(z)-$axis by $$; call this new frame $\{4\}.$

What is the final orientation of frame $\{4\}$ in the fixed frame $\{0\},R_{04}?$

$($b$)$ Suppose that the third step above is replace by the following: "Rotate $\{3\}$ about the vec$(z)-$axis of frame $\{3\}$ by $$; call this new frame $\{4\}."$ What is the final orientation of frame $\{4\}$ in the fixed frame $\{0\},R_{04}?$