From equation 9.5.8, with
(
)
1 1
1
3
ˆ
ˆ
e
e
e
ω
ω
ω
ω
=
+
=
+
D
ˆ
G
G
:
(
)
(
)
(
)
2
1
2
cos45
ω
ω
Ω =
−
=
D
From equation 9.6.12 …
(
)(
)
1
2
2
2
2
1
2
1
cos 45
5
φ
ω
ω
=
+
−
=
D
±
9.15
(
)
1 1
2
2
3
3
ˆ
ˆ
ˆ
N
c
c
e
e
e
ω
ω
ω
ω
= −
= −
+
+
G
G
Say the 3 axis is the symmetry axis,
3
s
I
I
=
,
1
2
I
I
I
=
=
For the third component of equations 9.3.5 …
3
3
0
s
c
I
ω
ω
−
=
+
±
ω
G
N
G
α
3
1
3
3
s
c
I
ω
ω
= −
±
(
)
3
3
ln
s
c
t
I
ω
ω
= −
D
(
)
3
3
s
ct
I
e
ω
ω
−
=
D
2
For the first two components of equations
9.3.5 …
(
)
1
1
2
3
s
c
I
I
ω
ω
ω ω
I
−
=
+
−
±
, and
(
)
2
2
1
3
s
c
I
I
I
ω
ω
ω ω
−
=
+
−
±
Rearranging terms and multiplying by
1
ω
and
2
ω
respectively …
(
)
2
1
1
1
1
2
3
0
s
c
I
I
I
ω ω
ω
ω ω ω
+
+
−
=
±
(
)
2
2
2
2
1
2
3
0
s
c
I
I
I
ω ω
ω
ω ω ω
+
−
−
=
±
Adding,
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 Fall '11
 JohnAnderson
 Work, tan α, ω 3e3, ω3

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