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‫Welcome back.

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‫So the task was to map the body frame coordinates to the inertia frame coordinates in 3-D using a rotation

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‫matrix, the vector in the body frame has three dimensions small X, Y, Z transposed.

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‫And the same vector in the inertia frame also has three dimensions big X, Y, Z, transpose.

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‫And by the way, the reason why I put transpose here is because I'm working with column vectors.

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‫K in reality, I'm talking about column vectors that look like this, but I can save space if I just

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‫write it down like this and it's the same thing, it's just more convenient to write it like this.

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‫But a role vector transposed will give you a column vector.

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‫And so if you want to go from a body frame representation to an inertial frame representation, you

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‫can use the vector matrix notation like this.

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‫This is the vector in the inertial frame and this is the vector in the body frame.

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‫And now the question is what's inside this rotation matrix that rotates the body frame with respect

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‫to the inertia frame about the Z axis?

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‫Let's see.

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‫Let's call it are subsets.

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‫And to fill in this matrix, we can first write down what we are trying to achieve in a different way

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‫like this.

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‫So can you fill in the gaps?

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‫If you haven't done it yet, then tried now yourself and then see the solution in the next video.