Assignment $1,$

ADVANCED DYNAMICS

$2024,$ semester $1$

Rotations of a fuhe

Consider a cube with sides length of $L=$I as is shown in Figure $2\mathrm{.}21.$ The corners of the cube are at $A(1,0,0),B(1,1,0),C(0,1,0),D(0,0,0),E(1,0,1),F(1,1,1),G(0,1,1),H(0,0,1).$ Let call this original configuration, the rest position.

a$.$ Turn the cube $45$ deg about the axis connecting point $D$ and the center of square EFGH and determine the coordinates of all corners in G$-$frame. $(10$ point$)$

b$.$ After the rotation in part a$,$ turn the cube $45$deg about the axis connecting point $D$ and the center of square ABFE and determine the coordinates of all corners in G$-$frame. $(20$ point$)$

c$.$ After the rotation in part b$,$ turn the cube $45$deg about the axis connecting point $D$ and the center of square BCGF and determine the coordinates of all corners in G$-$frame. $(30$ point$)$

d$.$ After the rotation in part $c,$ determine one axis and angle of rotation that turns the cube back to its original orientation. $(20$ point$)$

e$.$ Determine the intersection point of the axis of rotation of part $d$ with the cube. $(20$ point$)$