I'm a huge fan of that book, but am very glad you called it out as more people should know about it. there's also a great companion book "Functional Differentia

I'm a huge fan of that book, but am very glad you called it out as more people should know about it. there's also a great companion book "Functional Differential Geometry". My one caveat with that approach is it requires a very specific implementation of their library in MIT Scheme. There probably is a racket implementation by now, but it still looks like it's most small personal github projects. The automatic differentiation landscape has changed considerably since that book was written. I would love to eventually be able to put together something like a guide to Lagrangian mechanics with JAX.