User Tools


Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
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]
Line 187: Line 187:
 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
  
 $$ $$