‫Welcome back.
‫In this video, I want to forget about the transfer matrix for one second because I want to talk about
‫something else.
‫So it's going to be very quick.
‫In the last video, you learned how to connect this green reference frame vector to this red reference
‫frame vector.
‫It was this case here.
‫Then you learned how to connect the purple reference frame with the green reference frame, which was
‫this case here.
‫And those two connections allowed you to connect the purple reference frame with the red reference frame
‫that was attached to the drone.
‫And now how would you connect the true inertial frame, which is this white one?
‫How would you connected with the purple reference frame?
‫Well, now you are truly rotating about the inertial Z axis at an angle PSI, which means that if you
‫wanted to find some kind of quantity in the inertia frame, then you very simply had to multiply the
‫matrix or subset times the purple frame.
‫But since in the last video you found out how to connect the purple frame with the red body frame,
‫then what you can do now, you can take this entire thing here and you can just substitute this vector
‫with this.
‫And if you do that, then you can write this entire thing like this are Z times are Y, times are X
‫times the real body frame that is attached to the drone.
‫And now, look, isn't it familiar to you that's the exact same triple multiplication of those three
‫rotation matrices that we had before, because now here we are connecting the true inertial frame with
‫the true body frame.
‫Right.
‫We're connecting this with this.
‫And in the past, we discussed that this product is suitable for this convention when you rotate about
‫the fixed frame and it's also suitable for this convention when you rotate about the moving body frame.
‫But the rotation sequence is the opposite to the one that you have here.
‫And that's why we claimed that for our convention, this would be our rotation matrix product that would
‫connect our body frame with our inertial frame.
‫But now, as we went through this entire derivation, in order to find a transfer matrix as a bonus,
‫you can now also mathematically see that indeed, if you want to connect the body frame with the inertia
‫frame, then the rotation matrices indeed have to be in this order.
‫So this what we have done here is just another way to show that for this convention, this would be
‫the right rotation matrix product.
‫Now you can mathematically justify why this product is suitable for this convention in order to connect
‫the real body frame with the real inertial frame.
‫So I just wanted to get this out of the way.
‫And let's go back to the transfer matrix now.
‫See you in the next video.