1 00:00:00,390 --> 00:00:01,170 ‫Welcome back. 2 00:00:01,830 --> 00:00:10,650 ‫So let's now quantify the gyroscopic effect for our drone, so this is our drone here and one has a 3 00:00:10,650 --> 00:00:13,080 ‫positive angular rotation. 4 00:00:13,740 --> 00:00:26,730 ‫Also M3 and then M2 has a negative angular rotation and also in four has a negative angular rotation, 5 00:00:27,270 --> 00:00:28,260 ‫Omega four. 6 00:00:29,250 --> 00:00:37,740 ‫So before we quantify the gyroscopic effect, let's define a quantity called total angular velocity 7 00:00:37,740 --> 00:00:41,970 ‫of the propellers and let's just name it Omega. 8 00:00:42,880 --> 00:00:57,250 ‫And then we say that Omega equals omega one, minus Omega two, plus omega three and minus Omega four. 9 00:00:58,240 --> 00:01:07,970 ‫That's how you add the angular velocities of M one and two and three and four, respectively. 10 00:01:08,950 --> 00:01:18,160 ‫Note that you have to put minus signs in front of Omega two and Omega four because according to the 11 00:01:18,160 --> 00:01:20,240 ‫right hand rule, they are negative. 12 00:01:20,920 --> 00:01:32,500 ‫And so since Omega is our total angular velocity of the four murders, then, for example, if all of 13 00:01:32,500 --> 00:01:47,320 ‫them rotate at 50 radians per second in terms of magnitude, then it would be 50 minus 50, plus 50 14 00:01:47,830 --> 00:01:54,580 ‫and minus 50 equals zero radians per second. 15 00:01:55,460 --> 00:01:58,210 ‫So that would be the total quantity of Omega. 16 00:01:59,050 --> 00:02:02,740 ‫And remember, vector magnitudes are always positive. 17 00:02:03,430 --> 00:02:11,770 ‫So, for example, if you have a vector that is, for example, minus three meters per second, then 18 00:02:11,770 --> 00:02:21,700 ‫the magnitude of the vector still would be three meters per second because a magnitude doesn't care 19 00:02:21,700 --> 00:02:23,050 ‫about the direction. 20 00:02:23,500 --> 00:02:25,960 ‫A magnitude just tells you. 21 00:02:27,060 --> 00:02:36,780 ‫The strength of the vector or in other words, the length of this vector of this arrow, next, let's 22 00:02:36,780 --> 00:02:43,650 ‫write down the expression for the moment from the gyroscopic effect for each motor separately. 23 00:02:44,670 --> 00:02:50,370 ‫In the previous example, we had this structure and our disk rotated like this. 24 00:02:51,340 --> 00:02:58,180 ‫And then we rotated the entire structure like this at Alpha Dot radians per second. 25 00:02:59,170 --> 00:03:07,600 ‫In other words, we describe the angular rotation of our entire structure with this angular velocity 26 00:03:07,600 --> 00:03:08,210 ‫vector. 27 00:03:09,370 --> 00:03:16,360 ‫So if you think in terms of a drone now, then how would you describe the rotation of its structure? 28 00:03:17,200 --> 00:03:20,200 ‫Well, you can also use its angular velocities, right? 29 00:03:21,130 --> 00:03:30,160 ‫The drone can rotate about its three body frame, axis X, Y and Z, and the rotation about these axis 30 00:03:30,550 --> 00:03:33,400 ‫has some kind of angular velocity. 31 00:03:34,240 --> 00:03:36,640 ‫And we had a vector to describe that. 32 00:03:36,640 --> 00:03:45,720 ‫We had our angular velocity vector and it looked like this who had P, Q, R, radians per second. 33 00:03:46,450 --> 00:03:54,940 ‫So instead of Alpha Dot, now we're going to have this vector here and instead of a disk rotation, 34 00:03:56,020 --> 00:03:58,810 ‫we're going to have propellor rotations. 35 00:03:59,840 --> 00:04:07,760 ‫So let's call the moment that we get from the gyroscopic effect, thanks to more one, let's call it 36 00:04:07,760 --> 00:04:13,520 ‫like this m sup g r sub M one. 37 00:04:14,240 --> 00:04:24,680 ‫So he stands for the gyroscopic moment for M one more and well, for this structure that we had before 38 00:04:24,860 --> 00:04:33,100 ‫our moment equaled our Alpha Dot Cross H, which is the angular momentum of the disk. 39 00:04:33,980 --> 00:04:44,480 ‫And now we simply have the angular velocity vector in the body frame across the more one angular momentum 40 00:04:45,140 --> 00:04:46,610 ‫h sub M1. 41 00:04:47,680 --> 00:04:54,850 ‫And just to be clear, this vector here, this is the angular velocity vector for the entire drone. 42 00:04:55,750 --> 00:04:59,620 ‫It has P, Q and R radians per second. 43 00:05:00,310 --> 00:05:03,400 ‫It's how the entire drone rotates. 44 00:05:04,550 --> 00:05:10,760 ‫Like this, but this angular momentum vector, this only applies to more one. 45 00:05:11,940 --> 00:05:24,180 ‫So it's this one here, each one you can rewrite this equation like this w in the body frame cross GTP 46 00:05:24,180 --> 00:05:33,600 ‫P times Omega one, GTP is the rodders mass moment of inertia about its rotating axis. 47 00:05:34,650 --> 00:05:39,750 ‫And the major one is the angular velocity of our rotor. 48 00:05:40,690 --> 00:05:47,080 ‫And if you multiply them together, then you get the angular momentum of your M one. 49 00:05:48,700 --> 00:06:01,180 ‫So that was for more one for motor two, it's similar MS up G.R. sub M2 equals the drones angle velocity 50 00:06:01,180 --> 00:06:05,000 ‫in the body frame across H. 51 00:06:05,110 --> 00:06:07,270 ‫Sub M2 or. 52 00:06:08,570 --> 00:06:23,120 ‫W. in the body frame cross minus Jessopp T p times Omega two, and that's because four more to the angular 53 00:06:23,120 --> 00:06:26,030 ‫momentum is negative. 54 00:06:27,020 --> 00:06:28,490 ‫So that's the only difference. 55 00:06:29,330 --> 00:06:36,740 ‫Then for motor three, it would be the following, the angular velocity vector cross the angular momentum 56 00:06:36,740 --> 00:06:38,140 ‫vector for that Mowrer. 57 00:06:38,660 --> 00:06:40,970 ‫And by the way, these are also vectors here. 58 00:06:40,970 --> 00:06:54,530 ‫So I'm going to put arrows on top of the capital H and again W in the body frame cross J sup t p times 59 00:06:55,250 --> 00:07:05,760 ‫Omega three and finally you have M sub, G.R. sub and four equals W in the body frame. 60 00:07:05,780 --> 00:07:11,330 ‫Cross the angular momentum vector four and four equals. 61 00:07:12,170 --> 00:07:13,080 ‫And guess what. 62 00:07:13,700 --> 00:07:20,780 ‫Of course you're going to have minus J subtype times omega four. 63 00:07:21,830 --> 00:07:30,530 ‫And now I'm going to give you an exercise to do you know that this W in the body frame vector is this 64 00:07:30,530 --> 00:07:30,980 ‫one. 65 00:07:31,880 --> 00:07:33,730 ‫You have PK, you are here. 66 00:07:34,610 --> 00:07:48,680 ‫So what I would like you to do now, I would like you to find three by one vectors for each motor here 67 00:07:49,640 --> 00:07:50,390 ‫like this. 68 00:07:51,560 --> 00:08:00,590 ‫So I would like you to take this vector here and here and here and here, substitute them with P, Q, 69 00:08:00,590 --> 00:08:09,140 ‫R and cross them with these things here and let's see what you're going to get as a product. 70 00:08:10,010 --> 00:08:14,450 ‫So try and buy yourself and then I will show you the solution in the next video. 71 00:08:15,050 --> 00:08:15,890 ‫Thank you very much.