I don’t understand how they can accurately aim artillery. When they fire the whole machine moves a great deal and it would seem any calibration of its position would be lost.
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I’m not sure if its been mentioned, but wartime mathematicians were faced with this problem. You have a ‘boundary value problem’ i.e the bad guys are at the boundary (you dont want to shoot passed them do you?). But you only have information regarding your ‘initial conditions’ i.e you know what angle your mortar is facing. So how do we hit them?
The [Shooting Method](https://en.m.wikipedia.org/wiki/Shooting_method) is the answer to this. Its a way to numerically reduce the boundary value problem into an initial condition problem.
Warning: link contains differential equations
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