
397Motion of Rigid Bodies
© 2010 Taylor & Francis Group, LLC
TA A
or, equivalently,
−
=λ
.
This equation has a nontrivial solution if the determinant of the coefcients vanishes:
det
T
TTT
TT T
TTT
xx xy xz
yx yy yz
zx zy zz
−
()
=
−
−
−
λ
λ
λ
λ
1
=
.
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
may also be complex. Taking the complex
conjugate of
, we have
A
. Multiplying these equations by
and
, respect ...