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‫Welcome back.

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‫Well, in fact, you're rotating about the Z axis, right, both about the inertial and the body frame

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‫Z axis, because they're both aligned.

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‫So these are the reference frames in three dimensions.

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‫And if you look at them from the top, then it looks like this where both big and small Z pop out of

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‫the screen towards you.

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‫By the way, the convention for representing, if an arrow points towards you or away from you is the

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‫following.

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‫This one means that the arrow is pointing towards you.

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‫So this is like the tip of an arrow.

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‫This one means that the arrow is pointing into your paper sheet or into the screen away from you.

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‫So it's like the back of the arrow in our case, the easy access point towards you.

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‫But remember, we put the body frame on top of the inertia frame for visual purposes, but we can also

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‫put a body frame here.

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‫It doesn't matter for as long as the angle BPCI is the same.

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‫The only difference here is that now you're rotating only about the body frame Z axis and not about

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‫the inertia frames the axis, but the rotation matrix stays the same.

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‫So now knowing that a rotation of a body frame with respect to an inertial frame in 3D is nothing else

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‫but a rotation about the Z axis, would you be able to construct a rotation matrix about the Z axis

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‫in 3D?

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‫In other words, if you have some kind of vector in the body frame and you want to have this vector

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‫in the inertial frame and these are 3D vectors now and you know that they only rotate about the Z axis,

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‫will you be able to find this rotation matrix that only rotates about the Z axis?

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‫So this is your exercise tried yourself and then in the next video you will see the answer.

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‫Thank you very much.

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‫See you in the next video.