How can I calculate the trajectory of a payload fairing assuming that I have several data points of height or speed of rocket?
I'd like to know which topics are necessary to study this.
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A "classical" fairing is a ballistic object, meaning it has no active controls. You'll find that trying to model its tumbling path through a highly variable atmosphere exceeds our current computational capacity.
If you're thinking about the SpaceX fairing recovery techniques, be aware that there are some active controls, as explained in this space.SE question/answer.