‫Welcome back.
‫So let's remember what we had to do in order to get our state's space for that was our Newton oilor
‫form after rearranging the terms.
‫This is what you got.
‫And then this Lambda B here is.
‫Nothing else, but just a collection of these Lunda vectors, and now it's just going to become a substitution
‫and mathematical manipulation exercise.
‫You first substitute your net for a moment vector with your three separate relevant force moment vectors,
‫then you write out all your matrices as six by six matrices.
‫So I'm referring to this one and this one and also all your vectors, this one and this one as six by
‫one vectors.
‫And you do that to see all your state's inputs and time derivatives of the state's.
‫And then you just write out all vectors and matrices so that you would end up with six separate equations
‫like this.
‫You have six state time derivatives and then they all equal something.
‫That's what you need to end up with, and that will be your exercise now, try to write out the equations
‫in that form, you know, your Seeb matrix, your state vector, and you now also know your lambda vector,
‫which is essentially this.
‫So you have to rewrite these equations in a state based form.
‫But having all these terms inside your equations so you know what your lambda B vector is now and you
‫also know your mass and mass movement of inertia matrix.
‫It was this one where you had your diagonal elements, the first ones where the mass value and then
‫the other three diagonal elements were mass moments of inertia about the body frame, X, Y and Z axis.
‫And so if you take the inverse of that, then it will look like this.
‫So all these diagonal elements there will become one over those diagonal elements.
‫And of course, everything else is zeros.
‫And then this C v matrix, we covered that in the end of the previous section.
‫So you can look it up over there as well.
‫So knowing all that, tried to do it, tried to do this exercise, don't skip it because it's very important
‫that you do it yourself as well.
‫And I will do it for you in the next video so that you could check if you did it correctly.
‫So thank you very much and see you in the next video.