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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
397Motion of Rigid Bodies
© 2010 Taylor & Francis Group, LLC

TA A
or, equivalently,
TA
()
10
.
This equation has a nontrivial solution if the determinant of the coefcients vanishes:
det
T
TTT
TT T
TTT
xx xy xz
yx yy yz
zx zy zz
()
=
λ
λ
λ
λ
1

=
0
.
This cubic equation for A- has three roots that are either all real or one real and one complex con-
jugate pair. But for a symmetric tensor, the latter possibility can be ruled out. To see this, suppose
that λ is complex, and the corresponding eigenvector
A
may also be complex. Taking the complex
conjugate of

TA A
, we have

TA
A
**
. Multiplying these equations by
A
*
and
A
, respect ...
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Publisher Resources

ISBN: 9781466569980