That's the shocking thing. It's totally not hard in a Lisp. I could write the code for that symbolic derivation in an evening, tops. The hard part is the compi

That's the shocking thing. It's totally not hard in a Lisp. I could write the code for that symbolic derivation in an evening, tops. The hard part is the compiler. The somewhat hard part is the efficient numerical integrator (if you want good convergence and rapid integration). The symbolic manipulation is easy, once you know what you're doing. If you want to know what you're doing, it's sufficient to see how other people did it: https://mitpress.mit.edu/sites/default/files/titles/content/sicm_edition_2/book.html https://mitpress.mit.edu/sites/default/files/titles/content/... And if you haven't seen it: https://mitpress.mit.edu/sites/default/files/sicp/full-text/book/book-Z-H-16.html#%_sec_2.3.2 https://mitpress.mit.edu/sites/default/files/sicp/full-text/... If you're dumb like me, and can't write a compiler or an efficient numerical integrator in your spare time, having this interpreted and using a naive integrator is still good enough most of the time. Computers are fast. The authors of the above proved the motion of the solar system is chaotic with a very, very long, very, very precise numeric integration on hardware from decades ago, so they have super-fancy code. For the types of things I do, a dumb integration is fine. Once you've seen how it's done, and don't mind lower speed, that's trivial in any language with closures (e.g. Python or even JavaScript). If you want to swing a double-pendulum, or play around with the motion of a solar system over shorter durations, it's easy. And using the tool is even easier. Look at SICM (linked book). The things that look like code snippets are literally all the code you need. The system, if you want it: https://groups.csail.mit.edu/mac/users/gjs/6946/installation.html https://groups.csail.mit.edu/mac/users/gjs/6946/installation...