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‫Welcome back.

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‫And now we only have to get the rotation matrix that rotates about the x axis again in 2D, it looks

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‫like this when we rotate about the X axis, then we use the angle five.

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‫And as a reminder, when we rotated about the y axis, then the angle was theta.

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‫And when we rotated about the Z axis, then the angle was BPCI, but now it's PHY.

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‫And now we will simply follow the same procedure.

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‫The body frame X equals the inertia frame X, therefore you have a one here and you have zeros here.

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‫The body frame x axis does not contribute to the inertia frame Y and Z axis.

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‫Therefore we put zeroes here and now we will decompose the body frame Y and Z vectors.

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‫These are the body frame Y components and these are the body frame Z components.

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‫The horizontal component of the body frame y axis is cosine five times by the frame y.

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‫So you put cosine y here and the horizontal component of the body frame Z axis is negative, so it's

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‫minus sine five times by frame Z.

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‫The vertical component of the body frame y axis is small Y times sine phi and then finally the vertical

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‫component of the body frame z axis is small Z times cosine phi.

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‫And therefore this would be your rotation matrix when you only rotate about the x axis and note that

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‫your rotation matrix when you only rotated about the Z axis only had BPCI angles, when you only rotated

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‫about the Y axis, your rotation matrix only had theta angles.

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‫And now since you rotate about the x axis, you only have the PHI Angles inside the Matrix.

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‫And there you go.

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‫Thank you very much.

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‫And I'll see you in the next video.