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cs:localization:rotation:start [2017/01/22 02:41] Brian Moore |
cs:localization:rotation:start [2017/01/22 03:07] Brian Moore [Inverse Rotation] |
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| - | It is worth stating explicitly that $R^{-1} \neq R(-\psi,-\phi,-\theta)$. If you yaw, then pitch, then roll into an orientation, you //cannot// anti-yaw, then anti-pitch, then anti-roll from that orientation to get back to the origin. You'd have to anti-roll, then anti-pitch, then anti-yaw. It must be multiplied by its //transpose// $R^{\mathrm {T}}$. | + | It is worth stating explicitly that $R^{-1} \neq R(-\psi,-\phi,-\theta)$. If you yaw, then pitch, then roll into an orientation, you //cannot// anti-yaw, then anti-pitch, then anti-roll from that orientation to get back to the origin. You'd have to anti-roll, then anti-pitch, then anti-yaw. It must be rotated completely in reverse. It must be multiplied by its //transpose// $R^{\mathrm {T}}$. |
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| - | U \neg (R_{-\theta} R_{-\phi} R_{-\psi})(R_\theta R_\phi R_\psi) U \\ | + | U \neq (R_{-\theta} R_{-\phi} R_{-\psi})(R_\theta R_\phi R_\psi) U \\ |
| + | U = (R_{-\psi} R_{-\phi} R_{-\theta}) (R_\theta R_\phi R_\psi) U \\ | ||
| U = (R_{-\psi} (R_{-\phi} (R_{-\theta} R_\theta) R_\phi) R_\psi) U \\ | U = (R_{-\psi} (R_{-\phi} (R_{-\theta} R_\theta) R_\phi) R_\psi) U \\ | ||
| U = (R_{-\psi} (R_{-\phi} (I) R_\phi) R_\psi) U \\ | U = (R_{-\psi} (R_{-\phi} (I) R_\phi) R_\psi) U \\ | ||
