Angular Motion in the Space-Fixed Frame
Let's now consider angular motion in the presence of linear motion of the center of mass. In general, we have [270]
![$\displaystyle \underline{L}\eqsp \sum \underline{x}\times \underline{p}
$](http://www.dsprelated.com/josimages_new/pasp/img2961.png)
![$ \underline{p}$](http://www.dsprelated.com/josimages_new/pasp/img2685.png)
![$\displaystyle \underline{\tau}\eqsp \dot{\underline{L}} \eqsp \frac{d}{dt}\sum ...
...m (\underline{v}\times\underline{p}+ \underline{x}\times \dot{\underline{p}}).
$](http://www.dsprelated.com/josimages_new/pasp/img2962.png)
![$ \underline{v}\times \underline{p}=\underline{v}\times m\underline{v}=\underline{0}$](http://www.dsprelated.com/josimages_new/pasp/img2963.png)
![$\displaystyle \underline{\tau}\eqsp \dot{\underline{L}} \eqsp \sum \underline{x}\times \dot{\underline{p}}
\eqsp \sum \underline{x}\times \underline{f}
$](http://www.dsprelated.com/josimages_new/pasp/img2964.png)
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Euler's Equations for Rotations in the Body-Fixed Frame
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Body-Fixed and Space-Fixed Frames of Reference