It's impenetrable to you because you are missing a lot of background. There is a formulation of classical mechanics that is totally different from (and yet mathematically equivalent to) Newton's. It is based on the definition of a new quantity called the action (which is a very misleading term, but we're stuck with it because history) and the principle that particles move in such a way as to minimize this quantity. It turns out that it's easier to turn the crank on the math for complex mechanical systems when you formulate it in this way. If you want the gory details, Wikipedia is a good place to start:

https://en.wikipedia.org/wiki/Lagrangian_mechanics

and if you want to do a deep dive, there is this:

https://mitpress.mit.edu/9780262028967/

A free HTML version of this was available a while back, and probably still is, but I can't find it just now.