Here's a film that goes over a lot of the basics: "BASIC MECHANISMS IN FIRE CONTROL COMPUTERS" [1]. It's a 1953 US Navy instructional film explaining how mechanical fire control computers worked.
These machines took inputs giving the speed and direction the ship was traveling, the speed and direction the target was moving, the distance and direction to the target, the wind speed and direction, and other factors, and computed how to aim the guns to shell the target.
These old-school education videos are such a treat. One of my favorite is on differential gearing - https://www.youtube.com/watch?v=K4JhruinbWc (apologies about the clickbait title)
The Antikythera mechanism (https://en.wikipedia.org/wiki/Antikythera_mechanism) "variously dated to about 87 BC,[22] or between 150 and 100 BC,[13] or to 205 BC,[23][24]" -- may have been an early differential analyzer -- but that's a hypothetical conjecture...
I didn't see this covered in this article and I don't remember. How were the coefficients for these differential equations calculated?
Also, how useful were these? Today, I think most people use vector field plots because differential equations are so complicated. And I can't think of an easy way to get from the output of this machine to a vector field.
Here's a film that goes over a lot of the basics: "BASIC MECHANISMS IN FIRE CONTROL COMPUTERS" [1]. It's a 1953 US Navy instructional film explaining how mechanical fire control computers worked.
These machines took inputs giving the speed and direction the ship was traveling, the speed and direction the target was moving, the distance and direction to the target, the wind speed and direction, and other factors, and computed how to aim the guns to shell the target.
[1] https://www.youtube.com/watch?v=gwf5mAlI7Ug