off-diagonal terms in
? Consider the vector angular momentum (§B.4.14):
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
This all makes sense, but what about those
off-diagonal terms in
? Consider the vector angular momentum (§B.4.14):
![$\displaystyle \underline{L}\eqsp \mathbf{I}\,\underline{\omega}\eqsp
m\left[\begin{array}{ccc}
I_{11} & I_{12} & I_{13}\\ [2pt]
I_{21} & I_{22} & I_{23}\\ [2pt]
I_{31} & I_{32} & I_{33}
\end{array}\right]
\left[\begin{array}{c} \omega_1 \\ [2pt] \omega_2 \\ [2pt] \omega_3\end{array}\right]
$](img2911.png)
We see that the off-diagonal terms
correspond to a
coupling of rotation about
with rotation about
.
That is, there is a component of moment-of-inertia
that is
contributed (or subtracted, as we saw above for
![$ \underline{\omega}=[1,1,0]^T$](img2914.png){kind=small}
) when both 
and
are nonzero. These cross-terms can be eliminated by
diagonalizing the matrix [452],B.25as discussed further in the next section.
