Cous_Cous_Cous

This is a grammatically correct sentence. It is a misuse of an idiom but semantic/idiomatic checks are not trivial.

* There is a function L(q,q'), the Lagrangian. How do I compute this function? Does it have an analytical expression? How does it depend on p or F?

I tend to think of the Lagrangian as "something that someone defined that happens to be useful". In classical mechanics, the notion of total energy (kinetic plus potential) is something we can all understand. The Lagrangian, which is kinetic minus potential energy, looks strange but happens to observe unusually useful properties. If you integrate the Lagrangian of a point particle, it will always take the path that minimizes the integral. We call this integral the action and the universe seems to behave in a way that minimizes the action. I don't admit to have a deeper understanding of why this happens but every experiment ever done seems to observe this.

The equation after Fig. 19-3 gives an analytic expression for the action: https://www.feynmanlectures.caltech.edu/II_19.html

Different physical systems will have different Lagrangians but once formulated, the physical system will always behave in a way that minimizes the action. In principle, if you can formulate a Lagrangian for the universe, you can predict how it will behave because you know it will behave in a way that minimizes the action.

EDIT: Added more details.

I held a neptunium (20.45 g/cc) sphere once. It was about the size of a baseball and I hard the hardest time lifting it. It was like lifting a full gallon jug of milk when you think it's empty - you apply a force and it doesn't budge. I had to lift it as if I was lifting a stack of books to get it off the pedestal.