140 3 Coordinates
⎡
⎣
E 1
E 2
E 3
⎤
⎦ =
= R 3 (ω)R 1 (I)R 3 (Ω)
⎡
⎣
E 1
E 2
E 3
⎤
⎦ = R 2
π
2 − φ 0
R 3 (λ 0 )
⎡
⎣
e 1
e 2
e 3
⎤
⎦ =
=
⎡
⎣
e 1 0
e 2 0
e 3 0
⎤
⎦
(3.90)
Box 3.18 (Transformation between oblique frames of reference: first design, second design).
(i) E → E
2
4
E 1
E 2
E 3
3
5 = R 3 (ω)
2
4
E 1
E 2
E 3
3
5 ,
2
4
E 1
E 2
E 3
3
5 = R 1 (I)R 3 (Ω)
2
4
E 1
E 2
E 3
3
5 ,
(3.91)
2
4
E 1
E 2
E 3
3
5 = R 3 (ω)R 1 (I)R 3 (Ω)
2
4
E 1
E 2
E 3
3
5 .
(3.92)
(ii) e → e
0
2
4
e 1 0
e 2 0
e 3 0
3
5 = R 2
“ π
2
− φ 0
”
R 3 (λ 0 )
2
4
e 1
e 2
e 3
3
5 .
(3.93)
(iii) E = e, E
= e
0
2
4
E 1
E 2
E 3
3
5 = R 3 (ω)R 1 (I)R 3 (Ω)
2
4
E 1
E 2
E 3
3
5 = R 2
“ π
2
− φ 0
”
R 3 (λ 0 )
2
4
e 1
e 2
e 3
3
5 =
2
4
e 1 0
e 2 0
e 3 0
3
5
⇔
R 3 (ω)R 1 (I)R 3 (Ω) = R 2
“ π
2
− φ 0
”
R 3 (λ 0 ) .
(3.94)