Simple Example
Consider a mass at
. Then the mass moment of inertia
tensor is
![$\displaystyle \mathbf{I}\eqsp m \left(\left\Vert\,\underline{x}\,\right\Vert^2\...
...ay}{ccc}
0 & 0 & 0\\ [2pt]
0 & 1 & 0\\ [2pt]
0 & 0 & 1
\end{array}\right].
$](http://www.dsprelated.com/josimages_new/pasp/img2891.png)
![$ \underline{\omega}=[\omega,0,0]^T$](http://www.dsprelated.com/josimages_new/pasp/img2892.png)
![\begin{displaymath}
I \eqsp \underline{\tilde{\omega}}^T\mathbf{I}\,\underline{\...
...{array}{c} 1 \\ [2pt] 0 \\ [2pt] 0\end{array}\right]m \eqsp 0.
\end{displaymath}](http://www.dsprelated.com/josimages_new/pasp/img2893.png)
![$ \underline{\omega}=[0,1,0]^T$](http://www.dsprelated.com/josimages_new/pasp/img2894.png)
![$\displaystyle I \eqsp \underline{\tilde{\omega}}^T\mathbf{I}\,\underline{\tilde...
...]
\left[\begin{array}{c} 0 \\ [2pt] 1 \\ [2pt] 0\end{array}\right] \eqsp m x^2
$](http://www.dsprelated.com/josimages_new/pasp/img2895.png)
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Example with Coupled Rotations
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Angular Momentum Vector in Matrix Form
Consider a mass at
. Then the mass moment of inertia
tensor is