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Preclass exercise (not graded)
Problem 1:
Although
d
ˇ
I
dt
6
= 0 in general, show that
ω
·
d
ˇ
I
dt
·
ω
= 0
.
Hints: the inertia tensor takes the form
ˇ
I
=
3
X
i
=1
I
i
e
i
e
i
.
The principal moments of inertia
I
1
,I
2
,I
3
remain constant in time, since the rigid
body has a ﬁxed shape and structure. But the principal axes
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 Spring '11
 Tan
 mechanics, Inertia

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