[amatic]

Another interpretation of the name "analog computers" is that they compute by analogy - by simulating the problem in a different medium. When analog computers were created, the there were no digital computers to make the distinction between analog (continuous) vs digital (discrete). There were mechanical computers that used gears and shafts, and angular speed as the main variable; electronic computers that used voltages, there is a famous hydraulic computer that used water levels and rates of flow to represent variables, etc.

You start by examining your problem in mathematical terms and write down the differential equations that describe it. For example, you have a model of a car suspension with parameters for spring stiffness, damping etc. You put the model into the computer, and play with the parameters to see how things work. Not that different from modern simulations. The one advantage over modern simulations is that you might get a better "feel" for the system - or so the proponents of the analog used to say, before digital computers replaced them.