Euler angles(1) Euler angles describe a sequence of three rotations about different axes in order to align one coord system with a second coord system Rotate about za by a Rotate about yb by B Rotate about Xc by y ZG C B B B C coSa -sina cosb 0 sinB 100 R= sina cosa 0 R=010 D R=0 coSy -siny inB 0 cosB 0 siny cosy AR-BR ER SREuler Angles (1) Angles (1) Euler angles describe a sequence of three rotations about different axes in order to align one coord. system with a second coord. system.   = 0 0 1 sin cos 0 cos -sin 0 α α α α RAB Rotate about Z ˆ A byα Rotate about Y ˆ B by β Rotate about XC by γ ˆ ZA ˆ XA ˆ YA ˆ XB ˆ YB ˆ ZB ˆ α α ZB ˆ XB ˆ YB ˆ XC ˆ YC ˆ ZC ˆ β β ZC ˆ XC ˆ YD ˆ X D ˆ YC ˆ ZD ˆ γ γ   = β β β β -sin 0 cos 0 1 0 cos 0 sin RBC   = γ γ γ γ 0 sin cos 0 cos -sin 1 0 0 RCD R R R RCD BC AB AD =