‫Welcome back.
‫So let's now quantify the gyroscopic effect for our drone, so this is our drone here and one has a
‫positive angular rotation.
‫Also M3 and then M2 has a negative angular rotation and also in four has a negative angular rotation,
‫Omega four.
‫So before we quantify the gyroscopic effect, let's define a quantity called total angular velocity
‫of the propellers and let's just name it Omega.
‫And then we say that Omega equals omega one, minus Omega two, plus omega three and minus Omega four.
‫That's how you add the angular velocities of M one and two and three and four, respectively.
‫Note that you have to put minus signs in front of Omega two and Omega four because according to the
‫right hand rule, they are negative.
‫And so since Omega is our total angular velocity of the four murders, then, for example, if all of
‫them rotate at 50 radians per second in terms of magnitude, then it would be 50 minus 50, plus 50
‫and minus 50 equals zero radians per second.
‫So that would be the total quantity of Omega.
‫And remember, vector magnitudes are always positive.
‫So, for example, if you have a vector that is, for example, minus three meters per second, then
‫the magnitude of the vector still would be three meters per second because a magnitude doesn't care
‫about the direction.
‫A magnitude just tells you.
‫The strength of the vector or in other words, the length of this vector of this arrow, next, let's
‫write down the expression for the moment from the gyroscopic effect for each motor separately.
‫In the previous example, we had this structure and our disk rotated like this.
‫And then we rotated the entire structure like this at Alpha Dot radians per second.
‫In other words, we describe the angular rotation of our entire structure with this angular velocity
‫vector.
‫So if you think in terms of a drone now, then how would you describe the rotation of its structure?
‫Well, you can also use its angular velocities, right?
‫The drone can rotate about its three body frame, axis X, Y and Z, and the rotation about these axis
‫has some kind of angular velocity.
‫And we had a vector to describe that.
‫We had our angular velocity vector and it looked like this who had P, Q, R, radians per second.
‫So instead of Alpha Dot, now we're going to have this vector here and instead of a disk rotation,
‫we're going to have propellor rotations.
‫So let's call the moment that we get from the gyroscopic effect, thanks to more one, let's call it
‫like this m sup g r sub M one.
‫So he stands for the gyroscopic moment for M one more and well, for this structure that we had before
‫our moment equaled our Alpha Dot Cross H, which is the angular momentum of the disk.
‫And now we simply have the angular velocity vector in the body frame across the more one angular momentum
‫h sub M1.
‫And just to be clear, this vector here, this is the angular velocity vector for the entire drone.
‫It has P, Q and R radians per second.
‫It's how the entire drone rotates.
‫Like this, but this angular momentum vector, this only applies to more one.
‫So it's this one here, each one you can rewrite this equation like this w in the body frame cross GTP
‫P times Omega one, GTP is the rodders mass moment of inertia about its rotating axis.
‫And the major one is the angular velocity of our rotor.
‫And if you multiply them together, then you get the angular momentum of your M one.
‫So that was for more one for motor two, it's similar MS up G.R. sub M2 equals the drones angle velocity
‫in the body frame across H.
‫Sub M2 or.
‫W. in the body frame cross minus Jessopp T p times Omega two, and that's because four more to the angular
‫momentum is negative.
‫So that's the only difference.
‫Then for motor three, it would be the following, the angular velocity vector cross the angular momentum
‫vector for that Mowrer.
‫And by the way, these are also vectors here.
‫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
‫Omega three and finally you have M sub, G.R. sub and four equals W in the body frame.
‫Cross the angular momentum vector four and four equals.
‫And guess what.
‫Of course you're going to have minus J subtype times omega four.
‫And now I'm going to give you an exercise to do you know that this W in the body frame vector is this
‫one.
‫You have PK, you are here.
‫So what I would like you to do now, I would like you to find three by one vectors for each motor here
‫like this.
‫So I would like you to take this vector here and here and here and here, substitute them with P, Q,
‫R and cross them with these things here and let's see what you're going to get as a product.
‫So try and buy yourself and then I will show you the solution in the next video.
‫Thank you very much.