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Martin Dieblich
26 lines
1.9 KiB
TeX
26 lines
1.9 KiB
TeX
The transformation from euler angles $ \eu e$ to a rotational matrix depends on the order of rotation. Here, the default order is 321, which means first \Yawc{Yaw} (about the \emph{third} axis), then \Pitchc{Pitch} (the \emph{second} axis) and finally \Rollc{Roll}(the \emph{first} axis). Please note the important definition about perspectives (page \ref{Important definition}).
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\begin{equation}
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\mat R_m = \begin{pmatrix}
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cos(\Pitch)cos(\Yaw) & cos(\Pitch)sin(\Yaw) & -sin(\Pitch) \\
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sin(\Roll)sin(\Pitch)cos(\Yaw) - cos(\Roll)cos(\Yaw) & sin(\Roll)sin(\Pitch)sin(\Yaw) + cos(\Roll)cos(\Yaw) & sin(\Roll)cos(\Pitch) \\
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cos(\Roll)sin(\Pitch)cos(\Yaw) + sin(\Roll)sin(\Yaw) & cos(\Roll)sin(\Pitch)sin(\Yaw) - sin(\Roll)cos(\Yaw) & cos(\Roll)cos(\Pitch)
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\end{pmatrix}\end{equation}
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\inHfile{INT32\_RMAT\_OF\_EULERS(rm, e)}{pprz\_algebra\_int}
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\inHfile{INT32\_RMAT\_OF\_EULERS\_321(rm, e)}{pprz\_algebra\_int}
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\inHfile{FLOAT\_RMAT\_OF\_EULERS(rm, e)}{pprz\_algebra\_float}
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\inHfile{FLOAT\_RMAT\_OF\_EULERS\_321(rm, e)}{pprz\_algebra\_float}
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You can also choose the 312 definition (First \Yawc{Yaw}, then \Rollc{Roll} then \Pitchc{Pitch} $\Rightarrow \mat R(\Yaw) \mat R(\Roll) \mat R(\Pitch)$). Again, remember the different order and sign:
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\begin{equation}
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\mat R_m = \mat R(-\Pitch) \mat R(-\Roll) \mat R(-\Yaw)
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\end{equation}
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\begin{equation}
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\mat R_m = \begin{pmatrix}
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cos(\Pitch)cos(\Yaw)-sin(\Roll)sin(\Pitch)sin(\Yaw) & cos(\Pitch)sin(\Yaw) + sin(\Roll)sin(\Pitch)cos(\Yaw) & -cos(\Roll)sin(\Pitch) \\
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-cos(\Roll)sin(\Yaw) & cos(\Roll)cos(\Yaw) & sin(\Roll) \\
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sin(\Pitch)cos(\Yaw) + sin(\Roll)cos(\Pitch)sin(\Yaw) & sin(\Pitch)sin(\Yaw)-sin(\Roll)cos(\Pitch)cos(\Yaw) & cos(\Roll)cos(\Pitch)
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\end{pmatrix}\end{equation}
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\inHfile{INT32\_RMAT\_OF\_EULERS\_312(rm, e)}{pprz\_algebra\_int}
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\inHfile{FLOAT\_RMAT\_OF\_EULERS\_312(rm, e)}{pprz\_algebra\_float}
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\inHfile{DOUBLE\_RMAT\_OF\_EULERS\_312(rm, e)}{pprz\_algebra\_float}
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