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cs:localization:rotation:start [2018/04/29 11:24] Brian Moore [Complete Rotation] |
cs:localization:rotation:start [2018/04/29 11:25] (current) Brian Moore [Equivalent Rotations] |
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We often want to calculate where our vector is at after rotating first by $R_1$, then by $R_2$, and finally by $R_3$. If you recall from above, these complete Rotation matrices will behave exactly as the specific roll, pitch, and yaw matrices. That is to say, the rotations they perform are all relative to the fixed global $x,y,z$ axes. Which means that the rotation performed last, $R_3$, must be allowed to act on the vector first. | We often want to calculate where our vector is at after rotating first by $R_1$, then by $R_2$, and finally by $R_3$. If you recall from above, these complete Rotation matrices will behave exactly as the specific roll, pitch, and yaw matrices. That is to say, the rotations they perform are all relative to the fixed global $x,y,z$ axes. Which means that the rotation performed last, $R_3$, must be allowed to act on the vector first. | ||
- | Were we to tell our submarine's control system to make a relative goal of $R(\psi_1,\phi_1,\theta_1)$, and then once accomplishing it make another relative rotation $R(\psi_2,\phi_2,\theta_2)$, and then finally tell it to make a third relative rotation $R(\psi_3,\phi_3,\theta_3)$, we would calculate the result as | + | Were we to tell our submarine's control system to perform a relative rotation of $R(\psi_1,\phi_1,\theta_1)$, and then once accomplishing it make another relative rotation $R(\psi_2,\phi_2,\theta_2)$, and then finally tell it to make a third relative rotation $R(\psi_3,\phi_3,\theta_3)$, we would calculate the result as |
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