1 00:00:00,530 --> 00:00:01,250 ‫Welcome back. 2 00:00:02,120 --> 00:00:10,760 ‫And now let's just sum up all these moments together and we will get a total moment that is induced 3 00:00:10,760 --> 00:00:12,380 ‫from the gyroscopic effect. 4 00:00:13,110 --> 00:00:14,600 ‫Well, that's called this moment. 5 00:00:14,960 --> 00:00:19,330 ‫M sup g r like this. 6 00:00:20,210 --> 00:00:23,390 ‫The moment induced from gyroscopic effect. 7 00:00:24,380 --> 00:00:34,520 ‫It equals this moment from and won, so the moment induced from the gyroscopic effect, thanks to more 8 00:00:34,520 --> 00:00:34,970 ‫one. 9 00:00:36,070 --> 00:00:41,410 ‫Plus, the gyroscopic moment from model two, from model three. 10 00:00:42,500 --> 00:00:48,090 ‫And from more for and of course, we can rewrite it like this as well. 11 00:00:48,890 --> 00:00:50,530 ‫This is from model one. 12 00:00:51,200 --> 00:00:52,340 ‫This is this one. 13 00:00:53,240 --> 00:00:54,680 ‫This is from one or two. 14 00:00:54,830 --> 00:00:56,720 ‫So this one here. 15 00:00:57,890 --> 00:01:06,270 ‫This is from Morrisroe, so this one here, and this is from Moore for so it's this one here. 16 00:01:07,190 --> 00:01:15,680 ‫So what we're going to do now, we're going to sum up the first elements of each vector and let's see 17 00:01:15,680 --> 00:01:18,680 ‫what we're going to get from each vector. 18 00:01:18,690 --> 00:01:22,610 ‫We will take the first element and then we're going to sum them up. 19 00:01:23,610 --> 00:01:25,360 ‫So this will be from here. 20 00:01:26,220 --> 00:01:28,000 ‫This comes from here. 21 00:01:29,010 --> 00:01:34,020 ‫This comes from here and this comes from here. 22 00:01:35,020 --> 00:01:44,560 ‫You can factor out queue times GTP, because they are present in every term, then this entire thing 23 00:01:44,560 --> 00:01:55,120 ‫will look like this queue times, GTP Times and in the parentheses you have Omegle one minus Omega two 24 00:01:55,240 --> 00:02:00,970 ‫plus omega three and minus Omega four. 25 00:02:01,840 --> 00:02:06,450 ‫So you have simply factored out queue times GTP and that's what you get. 26 00:02:07,360 --> 00:02:08,730 ‫And now look at this. 27 00:02:08,950 --> 00:02:09,910 ‫What is this? 28 00:02:10,900 --> 00:02:14,350 ‫Well, it's the same thing like this one here. 29 00:02:15,440 --> 00:02:22,850 ‫It's the toll, some of the angle of velocities of all the propellers, so this is your total omega. 30 00:02:24,170 --> 00:02:26,710 ‫So you can actually write it down like this. 31 00:02:27,560 --> 00:02:40,550 ‫Q Times Jay t.P times, the summation sign from K equals one to four and then you're going to have minus 32 00:02:40,550 --> 00:02:48,050 ‫one to the power of K plus one and Omega K. 33 00:02:48,930 --> 00:02:49,920 ‫It makes sense, right? 34 00:02:50,750 --> 00:03:03,050 ‫This part is this part and so when you're K equals one then it would be minus one one plus one and then 35 00:03:03,050 --> 00:03:03,980 ‫Omega one. 36 00:03:04,730 --> 00:03:07,750 ‫So you will have an even power here which is two. 37 00:03:08,400 --> 00:03:18,770 ‫So this minus one becomes a plus one like this and then is just going to be omega one, which is a positive 38 00:03:18,770 --> 00:03:21,420 ‫Omega, which is what you have over here. 39 00:03:22,460 --> 00:03:33,050 ‫However, if your key is to then it would be minus one to plus one and then omega two. 40 00:03:33,980 --> 00:03:40,730 ‫So you will have an odd power here, minus one to the power of three. 41 00:03:41,540 --> 00:03:42,830 ‫Omega two. 42 00:03:43,770 --> 00:03:51,330 ‫And minus one to the power of three will give you minus one and then omega two, and that's what you 43 00:03:51,330 --> 00:03:52,520 ‫have over here. 44 00:03:53,550 --> 00:04:02,280 ‫And the same thing applies when K equals three, then this will become four, so you will have a positive 45 00:04:02,280 --> 00:04:08,180 ‫sign here times omega three, which is this case here. 46 00:04:09,180 --> 00:04:15,030 ‫And of course, if you're case for, then you would have five here. 47 00:04:15,030 --> 00:04:17,310 ‫So you will have an all power. 48 00:04:17,670 --> 00:04:21,810 ‫So you will have minus omega four. 49 00:04:22,970 --> 00:04:31,340 ‫So you can write it down like this, or you can very simply write down this thing like this, Queue 50 00:04:31,580 --> 00:04:36,290 ‫Times, Jessopp, Teep Times or Mega. 51 00:04:37,220 --> 00:04:47,000 ‫And so again, this mega is your total angular velocity vector when you sum up all the angles, velocities 52 00:04:47,000 --> 00:04:48,110 ‫of your propeller's. 53 00:04:49,390 --> 00:04:58,720 ‫So in the code, you can first perform this operation and then what you get here, it will go here, 54 00:04:58,750 --> 00:05:06,360 ‫which is what I did in the code, and now we're going to do the exact same thing for the second elements 55 00:05:06,370 --> 00:05:08,320 ‫of all these four vectors. 56 00:05:09,350 --> 00:05:12,500 ‫So first we take this, which is this one. 57 00:05:13,770 --> 00:05:22,170 ‫Then we take this, which is this one here, then we take this one, which is this element here, and 58 00:05:22,170 --> 00:05:25,680 ‫then we take this element, which is this one here. 59 00:05:26,520 --> 00:05:33,520 ‫And now we're going to factor it out like this, minus P times, Jayce up top. 60 00:05:34,650 --> 00:05:45,690 ‫And again, you will have Omegle one minus Omeonga two plus Omega three and minus Omega four like this. 61 00:05:46,620 --> 00:05:52,570 ‫Again, this entire thing is just an amalgam which we have over here. 62 00:05:53,520 --> 00:05:59,370 ‫And so that will be your final answer for the second elements. 63 00:05:59,370 --> 00:06:07,200 ‫If you sum them all up and if you sum up all the elements in the third element, then it will just be 64 00:06:07,200 --> 00:06:07,580 ‫zero. 65 00:06:08,460 --> 00:06:21,060 ‫And so that means that your total gyroscopic moment m sup g r equals Q Times GTP Times Omega, which 66 00:06:21,060 --> 00:06:30,780 ‫is the total omega, the sum of all the angular velocities of all the propeller's minus P GTP times, 67 00:06:31,080 --> 00:06:33,810 ‫the total Omega and zero. 68 00:06:34,350 --> 00:06:36,900 ‫And the units of course are Knewton meters. 69 00:06:37,890 --> 00:06:46,470 ‫And now the final step that we have to do, we have to put this gyroscopic moment into our force and 70 00:06:46,470 --> 00:06:57,560 ‫moment vector, let's call it Lunda in the body frame and are so gyroscopic force and movement vector. 71 00:06:58,560 --> 00:07:00,420 ‫So why don't you do it yourself? 72 00:07:00,870 --> 00:07:04,290 ‫And then in the next video, I will do it for you. 73 00:07:05,190 --> 00:07:06,060 ‫Thank you very much. 74 00:07:06,060 --> 00:07:06,870 ‫And see you there.