
387Motion of Rigid Bodies
© 2010 Taylor & Francis Group, LLC
which simplies considerably for the case of rotation about a single xed axis. For deniteness,
we choose the z-axis as the axis of rotation,
k. The components of the angular momentum in
Equation 12.32 are then
L
x
= I
xz
ω
z
, L
y
= I
yz
ω
z
, L
z
= I
z z
ω
z
, (12.34)
and the equations of motion (Equation 12.33) reduce to
N
IN
IN
I
x
e
xz zy
e
yz zz
e
zz
() () ()
(),(), (===
d
d
d
ωωωω
z
. (12.35)
If the rigid body is symmetrical about the z-axis, we have from Equation 12.25 that
II
R
xz yz zz
== =
0
2
,
α
where R
α
is the perpendicular distance from the axis of rotation to the mass element α, and it is ...