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()
333
123 2
1
0
I
II
ωω
ωωω
=+
−
±
Adding, 0
111
2 2 2
II I
ω
=+ +
±± ±
222
11
2 2
33
1
0
2
d
III
dt
+
From equation 9.2.5,
[]
rot
d
T
dt
=
0
rot
T
constant
=
Multiplying equations 9.3.5 by
I
,
22
I
, and
I
, respectively:
2
1123 3
2
0
I
−
±
I
2
2123 1
3
0
I
−
±
I
2
3123 2
1
0
I
−
±
I
Adding,
0
22 2
1
0
2
d
dt
+
From equation 9.2.4,
2
d
L
dt
=
0
2
L
constant
=
9.8
From equations 9.3.5 for zero torque …
2 3
3
2
0
I
−
±
13 1
3
0
I
−
±
From the perpendicular axis theorem,
312
I
=
+
231
0
I
I
±
132
0
I
I
=−
±
Multiplying by
1
1
I
and
2
2
I
, respectively:
123
0
±
0
±
Adding,
1
2
1
2
d
dt
0
=+ =
+
±±
12
constant
+=
If
I
I
=
, from the third of Euler’s equations …
( )
0
I
=
±
3
constant
=
9.9
(a) From symmetry …
3
s
I
I
=
and
I
=
=
From the perpendicular axis theorem,
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This note was uploaded on 01/06/2012 for the course PHYSICS 4360C taught by Professor Johnanderson during the Fall '11 term at UNF.
 Fall '11
 JohnAnderson
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