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‫Welcome back.

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‫Let's find our transfer matrix now, first of all, what we need to do, we need to write this vector,

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‫this vector and this vector like this, because if we do that, then we can factor them out.

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‫And so if you want to write this vector in terms of this vector, well, then you very simply have a

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‫matrix here, a three by three matrix, where you put one here and everything else is zero.

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‫So if you write it out, then you will have this vector.

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‫So they are equal, right.

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‫Similarly, if you want to write this vector in terms of this vector, then you have a matrix here where

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‫you have one here and everything else is zero.

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‫And finally, if you want to write this vector in terms of this vector, then you very simply have a

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‫matrix where you put one here and zeros everywhere else.

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‫It makes sense, right?

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‫If you write them out, then you will get these vectors here and here and here.

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‫And now it just becomes mechanical calculation, so if you rewrite this entire roll like this, where

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‫instead of this vector, you write it out like this and instead of this vector, you write it out like

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‫this instead of this one, you write it out like this, then this entire row equals the inverse of the

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‫transfer matrix times.

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‫Again, this vector, which is the same like this, this and this, and now you can factor them out.

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‫You can rewrite this entire roll like this where you just put this vector here, and so if you compare

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‫this part of the equation to this part of the equation, then since these two vectors are the same,

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‫that means that this part here in the parentheses has to be this the inverse of the transfer matrix.

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‫And so now you have to take the inverse of this rotation matrix r x, which is the same thing that the

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‫transpose of this matrix, because it's an all the normal matrix and the result would be this one and

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‫the same thing for this matrix.

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‫And if you multiply them together and take their inverse, this is what you need here, then you can

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‫rewrite it like this and that would be your result.

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‫So this is pure linear algebra here.

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‫And then what you need to do, you need to take the inverse of this rotation matrix and multiply it

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‫by this green three by three matrix, which is what I did here.

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‫And this is the result here.

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‫And you also have to take this thing here and multiply it by this purple three by three guy, which

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‫is what I did here.

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‫And that would be your result here.

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‫And now it's very easy to find the inverse of the transfer matrix since you know that it's this row

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‫here.

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‫Then the first term here will be this one, right.

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‫Then the second term here will be this one here, this entire term.

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‫And the result of it was here, this matrix.

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‫So you just put it here.

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‫This is your second term and your third term was this one here.

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‫And the result was this matrix here and it's this one.

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‫And so now you have the three terms and you add them together.

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‫And when you add them together, then this is what you will get.

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‫And finally, that's the inverse of your transfer matrix.

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‫And if you multiply this matrix by this time, derivative oilor angle vector, then you will get this

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‫peak.

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‫You are vector.