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‫Welcome back.

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‫So let's remember what we had to do in order to get our state's space for that was our Newton oilor

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‫form after rearranging the terms.

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‫This is what you got.

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‫And then this Lambda B here is.

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‫Nothing else, but just a collection of these Lunda vectors, and now it's just going to become a substitution

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‫and mathematical manipulation exercise.

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‫You first substitute your net for a moment vector with your three separate relevant force moment vectors,

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‫then you write out all your matrices as six by six matrices.

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‫So I'm referring to this one and this one and also all your vectors, this one and this one as six by

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‫one vectors.

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‫And you do that to see all your state's inputs and time derivatives of the state's.

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‫And then you just write out all vectors and matrices so that you would end up with six separate equations

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‫like this.

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‫You have six state time derivatives and then they all equal something.

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‫That's what you need to end up with, and that will be your exercise now, try to write out the equations

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‫in that form, you know, your Seeb matrix, your state vector, and you now also know your lambda vector,

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‫which is essentially this.

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‫So you have to rewrite these equations in a state based form.

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‫But having all these terms inside your equations so you know what your lambda B vector is now and you

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‫also know your mass and mass movement of inertia matrix.

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‫It was this one where you had your diagonal elements, the first ones where the mass value and then

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‫the other three diagonal elements were mass moments of inertia about the body frame, X, Y and Z axis.

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‫And so if you take the inverse of that, then it will look like this.

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‫So all these diagonal elements there will become one over those diagonal elements.

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‫And of course, everything else is zeros.

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‫And then this C v matrix, we covered that in the end of the previous section.

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‫So you can look it up over there as well.

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‫So knowing all that, tried to do it, tried to do this exercise, don't skip it because it's very important

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‫that you do it yourself as well.

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‫And I will do it for you in the next video so that you could check if you did it correctly.

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‫So thank you very much and see you in the next video.