‫Welcome back.
‫Well, in fact, you're rotating about the Z axis, right, both about the inertial and the body frame
‫Z axis, because they're both aligned.
‫So these are the reference frames in three dimensions.
‫And if you look at them from the top, then it looks like this where both big and small Z pop out of
‫the screen towards you.
‫By the way, the convention for representing, if an arrow points towards you or away from you is the
‫following.
‫This one means that the arrow is pointing towards you.
‫So this is like the tip of an arrow.
‫This one means that the arrow is pointing into your paper sheet or into the screen away from you.
‫So it's like the back of the arrow in our case, the easy access point towards you.
‫But remember, we put the body frame on top of the inertia frame for visual purposes, but we can also
‫put a body frame here.
‫It doesn't matter for as long as the angle BPCI is the same.
‫The only difference here is that now you're rotating only about the body frame Z axis and not about
‫the inertia frames the axis, but the rotation matrix stays the same.
‫So now knowing that a rotation of a body frame with respect to an inertial frame in 3D is nothing else
‫but a rotation about the Z axis, would you be able to construct a rotation matrix about the Z axis
‫in 3D?
‫In other words, if you have some kind of vector in the body frame and you want to have this vector
‫in the inertial frame and these are 3D vectors now and you know that they only rotate about the Z axis,
‫will you be able to find this rotation matrix that only rotates about the Z axis?
‫So this is your exercise tried yourself and then in the next video you will see the answer.
‫Thank you very much.
‫See you in the next video.