‫And now to get the transfer matrix itself, you just take the inverse of the inverse of the transfer
‫matrix and now you have to be careful because this is not an all the normal matrix.
‫It means that you cannot just take the transpose of it to get the inverse like you did with rotation
‫matrices.
‫You have to use traditional linear algebra methods for that or use a symbolic math tool such as Mathematica
‫Matlab or the sci fi library in Python.
‫And after you take the inverse of the inverse of the transfer matrix, you will find that your transferring
‫matrix looks like this, and that's the transfer matrix you've been looking for during all this time.
‫You now have a matrix that connects the changes of the Euler angles with respect to time to the angular
‫velocities in the body frame.
‫And that's the matrix that makes the connection.
‫And if you want to go back, then you have the inverse of it.
‫This matrix allows you to switch between these variables very conveniently.
‫Now, keep in mind that this transfer matrix is only exclusively valid for our convention, which is
‫R, sub Z, Y, X, using the oilor angle approach, meaning that we are rotating about the moving body
‫frame axis.
‫If you remember, then the rotation matrix for our convention was the same like for the convention are
‫sub X, Y, Z using the fixed angle approach.
‫But now thanks to the transfer matrix, you can see that it matters which one of those two you choose.
‫Their product of the rotation matrices might be the same, which was this one here.
‫This product was valid for both conventions.
‫However, the transfer matrix would be different for this fixed angle approach y because when you use
‫the fixed angle approach, then the path from inertial to body frame is different.
‫I have tried to draw a rotation sequence here for the convention are sub X, Y, Z for the fixed angle
‫approach.
‫So we first rotate about the inertial X axis, then about the inertial y axis and then about the inertial
‫axis.
‫And you can clearly see that in order to connect p q r angular velocity with Fido's standard and Poseidon's,
‫the transfer matrix would be different.
‫For example, in our case, our angular velocity p, which was the rotation about the body frame x axis
‫P radians per second was equal to fly dot radians per second.
‫However, in this approach here, fi, that would happen here.
‫Right.
‫But you can see that the direction here is different from the direction here because P is rotation about
‫the body frame x axis.
‫But here 5.0 is angular velocity about the inertial x axis.
‫Therefore here P cannot be equal to fly dot.
‫So this is one example Y you can already see why the transfer matrix for this convention will be different.
‫All right.
‫And this is all for the transfer matrix.
‫And in the next lecture, we will wrap up the kinematics part where we apply both our rotation and transfer
‫matrices to our specific situation.
‫Thank you very much.
‫And I'll see you in the next video.