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Classical Mechanics, Second Edition, 2nd Edition
book

Classical Mechanics, Second Edition, 2nd Edition

by Tai L. Chow
May 2013
Intermediate to advanced content levelIntermediate to advanced
639 pages
23h 12m
English
CRC Press
Content preview from Classical Mechanics, Second Edition, 2nd Edition
387Motion of Rigid Bodies
© 2010 Taylor & Francis Group, LLC
which simplies considerably for the case of rotation about a single xed axis. For deniteness,
we choose the z-axis as the axis of rotation,
ωω=
ˆ
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
t
IN
t
IN
t
I
x
e
xz zy
e
yz zz
e
zz
() () ()
(),(), (===
d
d
d
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
Im
R
xz yz zz
== =
0
2
,
αα
α
where R
α
is the perpendicular distance from the axis of rotation to the mass element α, and it is ...
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Publisher Resources

ISBN: 9781466569980