‫Welcome back.
‫And now let's just sum up all these moments together and we will get a total moment that is induced
‫from the gyroscopic effect.
‫Well, that's called this moment.
‫M sup g r like this.
‫The moment induced from gyroscopic effect.
‫It equals this moment from and won, so the moment induced from the gyroscopic effect, thanks to more
‫one.
‫Plus, the gyroscopic moment from model two, from model three.
‫And from more for and of course, we can rewrite it like this as well.
‫This is from model one.
‫This is this one.
‫This is from one or two.
‫So this one here.
‫This is from Morrisroe, so this one here, and this is from Moore for so it's this one here.
‫So what we're going to do now, we're going to sum up the first elements of each vector and let's see
‫what we're going to get from each vector.
‫We will take the first element and then we're going to sum them up.
‫So this will be from here.
‫This comes from here.
‫This comes from here and this comes from here.
‫You can factor out queue times GTP, because they are present in every term, then this entire thing
‫will look like this queue times, GTP Times and in the parentheses you have Omegle one minus Omega two
‫plus omega three and minus Omega four.
‫So you have simply factored out queue times GTP and that's what you get.
‫And now look at this.
‫What is this?
‫Well, it's the same thing like this one here.
‫It's the toll, some of the angle of velocities of all the propellers, so this is your total omega.
‫So you can actually write it down like this.
‫Q Times Jay t.P times, the summation sign from K equals one to four and then you're going to have minus
‫one to the power of K plus one and Omega K.
‫It makes sense, right?
‫This part is this part and so when you're K equals one then it would be minus one one plus one and then
‫Omega one.
‫So you will have an even power here which is two.
‫So this minus one becomes a plus one like this and then is just going to be omega one, which is a positive
‫Omega, which is what you have over here.
‫However, if your key is to then it would be minus one to plus one and then omega two.
‫So you will have an odd power here, minus one to the power of three.
‫Omega two.
‫And minus one to the power of three will give you minus one and then omega two, and that's what you
‫have over here.
‫And the same thing applies when K equals three, then this will become four, so you will have a positive
‫sign here times omega three, which is this case here.
‫And of course, if you're case for, then you would have five here.
‫So you will have an all power.
‫So you will have minus omega four.
‫So you can write it down like this, or you can very simply write down this thing like this, Queue
‫Times, Jessopp, Teep Times or Mega.
‫And so again, this mega is your total angular velocity vector when you sum up all the angles, velocities
‫of your propeller's.
‫So in the code, you can first perform this operation and then what you get here, it will go here,
‫which is what I did in the code, and now we're going to do the exact same thing for the second elements
‫of all these four vectors.
‫So first we take this, which is this one.
‫Then we take this, which is this one here, then we take this one, which is this element here, and
‫then we take this element, which is this one here.
‫And now we're going to factor it out like this, minus P times, Jayce up top.
‫And again, you will have Omegle one minus Omeonga two plus Omega three and minus Omega four like this.
‫Again, this entire thing is just an amalgam which we have over here.
‫And so that will be your final answer for the second elements.
‫If you sum them all up and if you sum up all the elements in the third element, then it will just be
‫zero.
‫And so that means that your total gyroscopic moment m sup g r equals Q Times GTP Times Omega, which
‫is the total omega, the sum of all the angular velocities of all the propeller's minus P GTP times,
‫the total Omega and zero.
‫And the units of course are Knewton meters.
‫And now the final step that we have to do, we have to put this gyroscopic moment into our force and
‫moment vector, let's call it Lunda in the body frame and are so gyroscopic force and movement vector.
‫So why don't you do it yourself?
‫And then in the next video, I will do it for you.
‫Thank you very much.
‫And see you there.