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‫Welcome back.

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‫So if you look straight into the x axis, then you should get something like this.

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‫This is for the positive rotation and this is for the negative rotation.

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‫So you can see that you can make three to the projections.

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‫However, no matter which one you choose, you're still rotating about one axis, either X, Y or Z

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‫axis.

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‫But when you work in 3D, then your body frame or your drone can have an orientation that requires you

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‫to rotate your body frame about more than one axis, like in this case here, the frame in red, it's

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‫the body frame.

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‫You see, you have your body frame, X, Y and Z axis.

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‫And here we have rotated the body frame about the Z axis, then about the Y axis and then about the

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‫X axis just to avoid to have too many arrows here.

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‫I've only taken one axis, the X axis, and I only tracked that in order to reach the body frame.

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‫So first we rotate the angle about the Z axis.

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‫So we go from here to here, let's call it small X prime.

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‫Then we rotate about the Y axis at an angle theta.

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‫So then this small X prime goes a little bit down diagonally, let's call it small X double prime.

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‫And then we rotate about the x axis and then angle fi and then this X double prime will move here.

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‫So one thing that we need to note here is that you won't reach this orientation if you only rotate about

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‫one axis.

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‫However, you can reach that orientation by rotating about all the three axis.

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‫And that is why in three D, you don't only have a your angle BPCI, which is rotating about the Z axis,

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‫you also have a pitch angle Seeta, which is rotating about the Y axis and you have a role angle phi

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‫which is rotating about the x axis.

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‫So here's another exercise for you.

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‫We have already seen how the rotation matrix in 3D looks like when you rotate about the Z axis.

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‫Now your job is to construct a three D rotation matrix that represents the body frame with respect to

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‫the inertial frame when their y axis overlap.

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‫And the same thing you have to find for the X axis as well.

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‫In other words, you have to find these matrices here.

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‫This matrix here would be for this case and this matrix here would be for this case here.

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‫When you look straight into the x axis and both the body frame and the inertial frame x axis overlap

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‫with each other.

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‫So just follow the same logic that we used to derive the rotation matrix about the Z axis.

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‫And you will see the solution in the next video.

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‫Thank you very much.

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‫And see you there.