# Computing the local orbital frame vector directions and angles of gyroscope direction in the satellite

In the context of the study of a cubesat (little satellite), I am asked to define the local orbital frame and compute the local orbital frame vector directions as a function of time (I have to use a little scritpt Matlab or Python) and get the coordinates of a gyroscop in the satellite.

Here the context :

For the part 2.1, I have found the following figures for geocentric inertial reference frame :

and local orbit frame :

I think that, for part 2.1, vector directions of local orbital frame are simply the directions of curvilinear coordinates for an ellipse ($$\vec{e_{r}}$$ and $$\vec{e_{\theta}}$$ vectors for polar coordinates and $$\vec{e_{z}}$$ orthogonal to $$\vec{e_{r}}$$ and $$\vec{e_{\theta}}$$), so an elliptic trajectory with these 3 basis vectors would be enough : is it correct ?

Now what about the part 2.2 "Kinematics", anyone could give some advices ?

Regards

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