|P is for Practical|
I'll try to present a module I'm working on in my free time, and if you (or another monk) are interested in it, I'll set up a repository where you can get the code.
My inspiration comes from a simulation software called stella which I used in school, but which is closed source and, iirc, rather expensive.
The idea is that you can create objects and specify their relation, which means that you can either say things like "acceleration = force / mass", or things like "velocity gains/looses by "acceleration"" (which is, mathematically, a derivation).
A simple example for a falling stone might be something like this:
This will output a parabolic curve for height, and an linear for velocity. This is trivial to calculate manually as well, but if you want to add things like air resistance it's very hard to do manually.
That means that you can model physical relations (and other things, but being a physicist I tend to forget them...) with only very little physical knowledge, and without knowing it you are actually writing down a differential equation.
Solving that isn't hard (my prototype does that with Math::RungeKutta), the real work is manage the objects, ensure that values aren't calculated multiple times (to boost efficiency), and to create a usable API.
Further along the way I see a serialization format (based on yaml, json, xml or the like), plotting of the results and perhaps a GUI.
And I'm targeting the "everything is a library" approach, in Perl term "everything is a Module", so that large parts of the application (especially the modelling backend) can easily be used by other programs.
Am working on this occasionally, and plan to release the first modules to cpan as soons they have a stable API (and are not too buggy).