‫Welcome back.
‫And now we only have to get the rotation matrix that rotates about the x axis again in 2D, it looks
‫like this when we rotate about the X axis, then we use the angle five.
‫And as a reminder, when we rotated about the y axis, then the angle was theta.
‫And when we rotated about the Z axis, then the angle was BPCI, but now it's PHY.
‫And now we will simply follow the same procedure.
‫The body frame X equals the inertia frame X, therefore you have a one here and you have zeros here.
‫The body frame x axis does not contribute to the inertia frame Y and Z axis.
‫Therefore we put zeroes here and now we will decompose the body frame Y and Z vectors.
‫These are the body frame Y components and these are the body frame Z components.
‫The horizontal component of the body frame y axis is cosine five times by the frame y.
‫So you put cosine y here and the horizontal component of the body frame Z axis is negative, so it's
‫minus sine five times by frame Z.
‫The vertical component of the body frame y axis is small Y times sine phi and then finally the vertical
‫component of the body frame z axis is small Z times cosine phi.
‫And therefore this would be your rotation matrix when you only rotate about the x axis and note that
‫your rotation matrix when you only rotated about the Z axis only had BPCI angles, when you only rotated
‫about the Y axis, your rotation matrix only had theta angles.
‫And now since you rotate about the x axis, you only have the PHI Angles inside the Matrix.
‫And there you go.
‫Thank you very much.
‫And I'll see you in the next video.