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Suppose we have an equation in inertial frame A.

[tex]\begin{equation}\frac{{}^Ad\bf{H}_C}{dt} = \bf{M}_C\end{equation}[/tex]

Now we want to switch to body fixed frame B. For this need to employ correction factor [itex]{}^A\bf\omega^B\times\bf{H}_B[/itex]. Why do we have this correction factor? How to derive this correction factor?

[tex]\begin{equation}\frac{{}^Bd\bf{H}_C}{dt} + {}^A\bf{\omega}^B\times\bf{H}_C = \bf{M}_C\end{equation}[/tex]

[tex]\begin{equation}\frac{{}^Ad\bf{H}_C}{dt} = \bf{M}_C\end{equation}[/tex]

Now we want to switch to body fixed frame B. For this need to employ correction factor [itex]{}^A\bf\omega^B\times\bf{H}_B[/itex]. Why do we have this correction factor? How to derive this correction factor?

[tex]\begin{equation}\frac{{}^Bd\bf{H}_C}{dt} + {}^A\bf{\omega}^B\times\bf{H}_C = \bf{M}_C\end{equation}[/tex]

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