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synced 2026-05-09 22:49:53 +08:00
Martin Dieblich
32 lines
1.2 KiB
TeX
32 lines
1.2 KiB
TeX
This function requires the euler angles e and also their derivative ed.\\
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\begin{equation}
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\ra{r} = \begin{pmatrix} p\\q\\r \end{pmatrix} =
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\eye \multiplication \eye \multiplication\begin{pmatrix} \dot{\Roll}\\0\\0 \end{pmatrix} +
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\mat R(\Roll)\multiplication \eye \multiplication\begin{pmatrix} 0\\\dot{\Pitch}\\0 \end{pmatrix} +
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\mat R(\Roll)\multiplication \mat R(\Pitch)\multiplication \begin{pmatrix} 0\\0\\\dot{\Yaw} \end{pmatrix}
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\end{equation}
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\begin{equation}
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\mat R(\Roll) = \begin{pmatrix}
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1 & 0 & 0 \\
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0 & cos(\Roll) & -sin(\Roll) \\
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0 & sin(\Roll) & cos(\Roll)
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\end{pmatrix}
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\end{equation}
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\begin{equation}
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\mat R(\Pitch) = \begin{pmatrix}
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cos(\Pitch) & 0 & sin(\Pitch) \\
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0 & 1 & 0 \\
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-sin(\Pitch) & 0 & cos(\Pitch)
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\end{pmatrix}
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\end{equation}
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\begin{equation}
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\ra r = \begin{pmatrix} p\\q\\r \end{pmatrix} =
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\begin{pmatrix}
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- \sin (\Roll) \dot{\Yaw} + \dot{\Roll} \\
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\sin (\Roll) \cos (\Pitch) \dot{\Yaw} + \cos (\Roll) \dot{\Pitch} \\
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\cos (\Roll) \cos (\Pitch) \dot{\Yaw} - \sin (\Roll) \dot{\Pitch} \\
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\end{pmatrix}
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\end{equation}
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\inHfile{INT32\_RATES\_OF\_EULERS\_DOT(r, e, ed)}{pprz\_algebra\_int}
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\inHfile{INT32\_RATES\_OF\_EULERS\_DOT\_321(r, e, ed)}{pprz\_algebra\_int}
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