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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
407Motion of Rigid Bodies
© 2010 Taylor & Francis Group, LLC
I
11
+ I
12
tan θ = I, I
12
+ I
22
tan θ = I tan θ.
Eliminating I from these two equations, we find
(I
22
I
11
)tan θ = I
12
(tan
2
θ − 1)
from which we obtain
tan2
2
12
11 22
θ=
I
II
where we have used the identity tan2 θ = 2 tan θ/(1 − tan
2
θ).
In the interval 0° to 180°, there are two values of θ, differing by 90°, that satisfy Equation 12.76.
These two values of θ give the directions of the two principal axes in the xy-plane.
A body whose three principal moments of inertia are all different is called an asymmetrical top.
If two are equal, it is termed a symmetrical top. In this case, the direc
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Publisher Resources

ISBN: 9781466569980