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In Siouris's Missile Guidance and Control Systems, it is stated that the angle of attack can be approximated in a 3DoF (degrees of freedom) simulation by the following equation:

Siouris, Missile Guidance and Control Systems page 497

Siouris, Missile Guidance and Control System page 497

I know that ECI refers to the Earth Centered Inertial Frame. The only thing I don't understand is what this pointing vector, and its magnitude meant to be. It is not the thrust vector because the units do not match up (m for meters, otherwise it would be N for Newtons which is used commonly in the book). And also, if it is a pointing vector, why would it even have units?

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    $\begingroup$ Could it be the direction in which the missile is pointing? $\endgroup$
    – Jim
    Commented Dec 17, 2021 at 16:00

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Indeed the pointing vector $R_{NT}$ is the direction that the missile is pointing in, as @Jim mentions in a comment. Which is not necessarily in the direction of the velocity vector, in which case the angle of attack would be zero.

The angle of the two vectors can be computed via the cosine rule, as explained in the wikihow. The pointing vector has units of length - it floats in space, but transplanted to the centre of the earth will determine a distance in 3 dimensions.

And the magnitude of vector (x,y,z) is $ \sqrt{x^2 + y^2 + z^2}$

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    $\begingroup$ Confirmed by the book: "The model assumes that the pointing vector and the missile body-axis are the same." $\endgroup$
    – mins
    Commented Dec 18, 2021 at 13:03
  • $\begingroup$ So does this mean that I can treat the rocket thrust vector as the missile pointing vector as a simplified assumption? $\endgroup$
    – alexmesa
    Commented Dec 27, 2021 at 9:33
  • $\begingroup$ @alexmesa Yes indeed. On average, the thrust vector will point in the body axis. $\endgroup$
    – Koyovis
    Commented Dec 27, 2021 at 10:37

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