‫Welcome back.
‫Let's now compute the gyroscopic moment for model one.
‫To do that, you first take the angular velocity vector, which is P, Q and R, and you cross it with
‫an angular momentum vector of more one and the angular momentum vector of more one is in the direction
‫of its body frame Z axis.
‫So the rest of the dimensions are zero.
‫And that's of course, the propeller's body frame Z axis, not the Jones body frame Z axis, even though
‫actually they are in the same direction.
‫And now you know the drill.
‫You have this matrix and you take the determinant of it.
‫This would be the eye component then minus J.
‫This would be the J component and then plus K and that would be your key component.
‫And so if you do this to buy to determine it's here, then what you will get is this.
‫Q Time's up H one minus J-P times H one and then plus K times zero.
‫And it makes sense that this final term is zero.
‫That's because the model one angular momentum vector is in the same direction, like the drones rotation
‫about its body frame Z axis.
‫So if this is your drone's body frame Z axis here and this is your M1 propeller's body frame, Z axis,
‫which is this one.
‫So let's call it H one, then you can see that the rotation of both the drones body frame Z axis at
‫R radians per second has the vector in the same direction that the model one has in terms of its angular
‫momentum vector.
‫They're both in the same direction, so they are parallel.
‫And you already know what happens when you cross two parallel vectors with each other.
‫If it's this, then it's going to be zero or if it's even this, then it's going to be zero as well,
‫because still the vectors are parallel to each other.
‫And that's why this final term here is zero.
‫And if you put it in English, then what it really means is that since your propellers are attached
‫to the drone in such a way that the.
‫The rotation vectors are parallel to the drones, but from Z.
‫Access, that means that if you rotate your drone about the body from Z axis, then there will be no
‫gyroscopic effect.
‫Because the angular momentum vectors from the robber's.
‫Will not change their direction.
‫That's why the your rotation will not cause gyroscopic effect.
‫However, the roll and pitch rotations, they will cause a gyroscopic effect because that will cause
‫the direction change of the motors, angular momentum vectors.
‫Brooke, you can now rewrite this entire thing like this Q H one minus P times, H, one and zero,
‫and since it's a moment, then its unit is Knewton times meeta like this.
‫So that's four more one.
‫That's the moment vector induced from the gyroscopic effect because of more one propeller rotation.
‫If you now do it for other motors, then it looks like this.
‫This is the final answer for more to this is four more three and this is four more for.
‫And now let's replace the H.
‫Vector's with Jessopp, TPE and the Megas.
‫This will be four more one here in red.
‫This will be for my daughter to remember now you're Amiga is negative, so you have to take that into
‫account.
‫So you will end up with this vector here for murder three.
‫This is your answer and for more for this is the answer.
‫And again, you have to take into account that your mega your angular velocity for the propeller four
‫is negative.