[mnemonicsloth]

I'm not avoiding mathematics. I used to be a mathematician. The math is the whole point.

In the mechanics library that comes with the book (which I'm building on in my own work), functions can take either numerical or symbolic values. If you have a computation involving symbolic values, you can manipulate it just like you would with pencil and paper (except you can operate at a higher level of abstraction, never get writer's cramp, and never have to laboriously recopy line after line of symbols to make sure you got the right number of minus signs). If, as so often happens, you find yourself up against an intractable integral, you pass the whole thing to a numerical solver and get a number back right away. With enough calculations you can build up a qualitative understanding of the system's behavior. My understanding is that this is what mechanics people do all day, but not how mechanics is taught to newcomers.