Non-physicist here. Was hoping this would do something for me, but unfortunately... Very first line, I look up "Lagrangian" to see what L means, and I get ten different definitions: https://en.wikipedia.org/wiki/Lagrangian. I'm guessing it's the one that says kinetic minus potential energy, but that seems arbitrary (unlike the sum which would be total energy). Couldn't this be more specific?
Most of the other lines have terms/constants/variables that I've never heard of or don't remember from school, and usually it's "Lagrangian" again. I don't know what it means to fix, restrict, yield, or complete a Lagrangian. I could keep reading about that, but at this point I don't think I'm learning physics the right way. If there's one thing I remember from class, it's that there aren't many shortcuts here; usually you have to start at fundamentals and prove your way up.
Also, idk how entropy ≥ (some constant) implies thermodynamics, and seems the physicists here don't see it either.
> I'm guessing it's the one that says kinetic minus potential energy, but that seems arbitrary
It is arbitrary, in some sense: Lagrangians are specifications of a physical system in the same way that laws of motion are. Instead of directly describing a trajectory as the solution to some set of differential equations, the Lagrangian approach describes it as a stationary point (an extremum or a saddle point) of the action, which is the integral of the Lagrangian over time. The resulting equations of motion are then given by the Euler-Lagrange equation. L = K - V is (one formulation of) the Lagrangian for a system that obeys Newton's laws. Other systems have other Lagrangians, from which we get other laws of motion.
The other important formulation of classical mechanics is the Hamiltonian one, which very roughly speaking reparameterizes the Euler-Lagrange equation in terms of (generalized) positions and momenta, instead of just position. This turns your n-dimensional second order differential equation into a 2n-dimensional first order one, which is often more convenient to work with.
For simple "ideal billiard balls in a vacuum" situations it makes very little difference what approach you use, but Newtonian mechanics generalizes poorly. All of modern physics is based on the Lagrangian and Hamiltonian approaches.
"The theoretical minimum" series by Leonard Susskind et al. (along with the video series in YT) is a supergentle introduction & gloss of this whole table. If you stick to the books you'll never have to read popsci crap, again, except to join in with the eye rolling.
Most of the other lines have terms/constants/variables that I've never heard of or don't remember from school, and usually it's "Lagrangian" again. I don't know what it means to fix, restrict, yield, or complete a Lagrangian. I could keep reading about that, but at this point I don't think I'm learning physics the right way. If there's one thing I remember from class, it's that there aren't many shortcuts here; usually you have to start at fundamentals and prove your way up.
Also, idk how entropy ≥ (some constant) implies thermodynamics, and seems the physicists here don't see it either.