1 00:00:00,450 --> 00:00:01,240 ‫Welcome back. 2 00:00:01,590 --> 00:00:08,040 ‫In this video, I want to forget about the transfer matrix for one second because I want to talk about 3 00:00:08,040 --> 00:00:08,940 ‫something else. 4 00:00:09,330 --> 00:00:10,620 ‫So it's going to be very quick. 5 00:00:11,100 --> 00:00:20,460 ‫In the last video, you learned how to connect this green reference frame vector to this red reference 6 00:00:20,460 --> 00:00:21,360 ‫frame vector. 7 00:00:21,900 --> 00:00:23,430 ‫It was this case here. 8 00:00:24,090 --> 00:00:31,110 ‫Then you learned how to connect the purple reference frame with the green reference frame, which was 9 00:00:31,110 --> 00:00:32,160 ‫this case here. 10 00:00:32,700 --> 00:00:39,870 ‫And those two connections allowed you to connect the purple reference frame with the red reference frame 11 00:00:39,870 --> 00:00:41,920 ‫that was attached to the drone. 12 00:00:42,570 --> 00:00:48,930 ‫And now how would you connect the true inertial frame, which is this white one? 13 00:00:49,350 --> 00:00:51,960 ‫How would you connected with the purple reference frame? 14 00:00:52,440 --> 00:01:01,770 ‫Well, now you are truly rotating about the inertial Z axis at an angle PSI, which means that if you 15 00:01:01,770 --> 00:01:10,110 ‫wanted to find some kind of quantity in the inertia frame, then you very simply had to multiply the 16 00:01:10,110 --> 00:01:15,380 ‫matrix or subset times the purple frame. 17 00:01:15,960 --> 00:01:23,820 ‫But since in the last video you found out how to connect the purple frame with the red body frame, 18 00:01:24,360 --> 00:01:33,150 ‫then what you can do now, you can take this entire thing here and you can just substitute this vector 19 00:01:33,750 --> 00:01:34,500 ‫with this. 20 00:01:34,980 --> 00:01:44,910 ‫And if you do that, then you can write this entire thing like this are Z times are Y, times are X 21 00:01:45,450 --> 00:01:50,310 ‫times the real body frame that is attached to the drone. 22 00:01:50,820 --> 00:01:59,700 ‫And now, look, isn't it familiar to you that's the exact same triple multiplication of those three 23 00:01:59,940 --> 00:02:08,790 ‫rotation matrices that we had before, because now here we are connecting the true inertial frame with 24 00:02:08,790 --> 00:02:10,020 ‫the true body frame. 25 00:02:10,650 --> 00:02:11,160 ‫Right. 26 00:02:11,880 --> 00:02:14,370 ‫We're connecting this with this. 27 00:02:14,850 --> 00:02:23,580 ‫And in the past, we discussed that this product is suitable for this convention when you rotate about 28 00:02:23,580 --> 00:02:32,340 ‫the fixed frame and it's also suitable for this convention when you rotate about the moving body frame. 29 00:02:32,340 --> 00:02:37,320 ‫But the rotation sequence is the opposite to the one that you have here. 30 00:02:37,860 --> 00:02:48,090 ‫And that's why we claimed that for our convention, this would be our rotation matrix product that would 31 00:02:48,090 --> 00:02:51,170 ‫connect our body frame with our inertial frame. 32 00:02:51,780 --> 00:03:00,960 ‫But now, as we went through this entire derivation, in order to find a transfer matrix as a bonus, 33 00:03:00,960 --> 00:03:09,150 ‫you can now also mathematically see that indeed, if you want to connect the body frame with the inertia 34 00:03:09,150 --> 00:03:14,410 ‫frame, then the rotation matrices indeed have to be in this order. 35 00:03:14,970 --> 00:03:25,410 ‫So this what we have done here is just another way to show that for this convention, this would be 36 00:03:26,160 --> 00:03:28,830 ‫the right rotation matrix product. 37 00:03:29,460 --> 00:03:38,010 ‫Now you can mathematically justify why this product is suitable for this convention in order to connect 38 00:03:38,220 --> 00:03:42,030 ‫the real body frame with the real inertial frame. 39 00:03:42,660 --> 00:03:45,180 ‫So I just wanted to get this out of the way. 40 00:03:45,570 --> 00:03:48,820 ‫And let's go back to the transfer matrix now. 41 00:03:49,200 --> 00:03:50,370 ‫See you in the next video.