‫Welcome back.
‫So if you look straight into the x axis, then you should get something like this.
‫This is for the positive rotation and this is for the negative rotation.
‫So you can see that you can make three to the projections.
‫However, no matter which one you choose, you're still rotating about one axis, either X, Y or Z
‫axis.
‫But when you work in 3D, then your body frame or your drone can have an orientation that requires you
‫to rotate your body frame about more than one axis, like in this case here, the frame in red, it's
‫the body frame.
‫You see, you have your body frame, X, Y and Z axis.
‫And here we have rotated the body frame about the Z axis, then about the Y axis and then about the
‫X axis just to avoid to have too many arrows here.
‫I've only taken one axis, the X axis, and I only tracked that in order to reach the body frame.
‫So first we rotate the angle about the Z axis.
‫So we go from here to here, let's call it small X prime.
‫Then we rotate about the Y axis at an angle theta.
‫So then this small X prime goes a little bit down diagonally, let's call it small X double prime.
‫And then we rotate about the x axis and then angle fi and then this X double prime will move here.
‫So one thing that we need to note here is that you won't reach this orientation if you only rotate about
‫one axis.
‫However, you can reach that orientation by rotating about all the three axis.
‫And that is why in three D, you don't only have a your angle BPCI, which is rotating about the Z axis,
‫you also have a pitch angle Seeta, which is rotating about the Y axis and you have a role angle phi
‫which is rotating about the x axis.
‫So here's another exercise for you.
‫We have already seen how the rotation matrix in 3D looks like when you rotate about the Z axis.
‫Now your job is to construct a three D rotation matrix that represents the body frame with respect to
‫the inertial frame when their y axis overlap.
‫And the same thing you have to find for the X axis as well.
‫In other words, you have to find these matrices here.
‫This matrix here would be for this case and this matrix here would be for this case here.
‫When you look straight into the x axis and both the body frame and the inertial frame x axis overlap
‫with each other.
‫So just follow the same logic that we used to derive the rotation matrix about the Z axis.
‫And you will see the solution in the next video.
‫Thank you very much.
‫And see you there.