‫Welcome back.
‫So the task was to map the body frame coordinates to the inertia frame coordinates in 3-D using a rotation
‫matrix, the vector in the body frame has three dimensions small X, Y, Z transposed.
‫And the same vector in the inertia frame also has three dimensions big X, Y, Z, transpose.
‫And by the way, the reason why I put transpose here is because I'm working with column vectors.
‫K in reality, I'm talking about column vectors that look like this, but I can save space if I just
‫write it down like this and it's the same thing, it's just more convenient to write it like this.
‫But a role vector transposed will give you a column vector.
‫And so if you want to go from a body frame representation to an inertial frame representation, you
‫can use the vector matrix notation like this.
‫This is the vector in the inertial frame and this is the vector in the body frame.
‫And now the question is what's inside this rotation matrix that rotates the body frame with respect
‫to the inertia frame about the Z axis?
‫Let's see.
‫Let's call it are subsets.
‫And to fill in this matrix, we can first write down what we are trying to achieve in a different way
‫like this.
‫So can you fill in the gaps?
‫If you haven't done it yet, then tried now yourself and then see the solution in the next video.