Yes- There are many analogs which are useful- for example, analysis of
mechanical and acoustic systems in terms of electric circuit analysis.
Analogues are great for visualization- only where they fit and one must
know the limits of the fit. In the above cases, the equations are
essentially the same.
Analogue computers are another thing
Ive worked with them- I like them for the ability to play with
parameters and get the results- far more fun than digital computers as
one can twitch a parameter and immediately see the result. In practice,
they are basically op-amps set up to sum and integrate. In complex
problems you are limited by the op-amps available and the setup can be a
real pain in the ass. New problem but want to keep the old one?- need to
store the wiring board of the old problem and set up another. I have
used conductive paper to evaluate fields (2D) or electrolytic tanks
(3D)- cumbersome and a lot of drawing of equipotentials and flow lines
using what was called "curvilinear squares" I have also used a Network
analyser for power system load flow and stability studies(and designed a
way to automate this on one such device). The advantage was that you
thought about what you were doing. The disadvantage was that a lot of
equipment and very many man hours were required for the setup and
analysis of one system as well as the limitations of such systems.
Digital methods now allow the solution of problems beyond the scope of
the largest of the analogue machines- and do as much or more than these
devices could do, in a fraction of the time, using a reasonably good
home computer. Analogue computers for situations as encountered now,
involving thousands of simultaneous non- linear equations and possibly
throwing in a few hundred non-linear DEQ's, just can't cope in terms of
time and cost. This was realized 60 years ago in the power industry. The
geeks won because one cando much more at far less cost in $ and time.