So, a taste:

https://groups.csail.mit.edu/mac/users/gjs/6946/sicm-html/bo...

"1.5.2 Computing Lagrange's Equations

The procedure for computing Lagrange's equations mirrors the functional expression (1.18), where the procedure Gamma implements :58

   (define ((Lagrange-equations Lagrangian) q)
       (- (D (compose ((partial 2) Lagrangian) (Gamma q)))
            (compose ((partial 1) Lagrangian) (Gamma q))))"

Maybe more readable version:

https://tgvaughan.github.io/sicm/toc.html

Source: https://github.com/tgvaughan/sicm