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‫Just to make this section more complete, I want to rewrite our dynamic's equations in a slightly different

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‫form.

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‫I have seen both forms in the literature and I want to make sure that you recognize them both and realize

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‫that they are actually the same thing.

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‫So you can rewrite this entire thing.

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‫Like this and pay attention that this m super be now it's this matrix here.

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‫All right.

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‫So it's not a moment.

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‫It's a mass and mass moment of inertia matrix this six by six matrix.

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‫This is what it is.

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‫Then this vector here, it's this then this entire second term here.

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‫Which appears because your body frame is rotating with respect to your initial frame, it's sometimes

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‫in the literature rewritten like this and then this lumbar superscript B, it's this one here where

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‫you have your net force and net moment vectors.

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‫So the only big difference here is that they have taken this second term that appears because your body

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‫frame is rotating and they have rewritten it in a different way.

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‫Where this sea superscript B is a six by six matrix and then this small V, B is a six by one vector

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‫that contains information about the translational motion velocities in the body frame you the and W

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‫and the angular velocities in the body frame as well, P, Q and R.

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‫And so this c.B matrix ends up being this one here, the six by six matrix and then this V is this vector

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‫here.

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‫And to get this form, it's actually not that hard.

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‫All you have to do, you just have to apply cross product like we learned before.

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‫So you first take this one here.

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‫You will have a three by one vector cross and then the other term it will also be a three by one vector

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‫and then you apply the cross product to it.

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‫If you remember, you had your three by three matrix.

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‫That looks something like this, and then you took the determinant of it, and then you would find your

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‫cross product and then you would do the same thing for this one, and then you would just manipulate

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‫your variables in such a way that in all cases you extract your P, Q, R elements.

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‫So this is what I have seen in the literature, and I just wanted to point it out so that when you see

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‫it in the literature, so that you would know that it's actually the same thing, it's just you take

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‫this second term and then you apply across product of it.

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‫You do some algebraic manipulations and then you put this form into this form.

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‫But they're the same thing.

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‫There's nothing different here is just you apply mathematics to reformulate this term and put it like

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‫this.

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‫In fact, why don't you try it as an exercise and I'm going to give you the solutions in the next video,

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‫try to put this form into this form.

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‫See you in the next video.