Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. Plural form of Lagrangian.
Etymologies
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Examples

Schmidt and Lipson's algorithm was able to converge on the Hamiltonians, Lagrangians and force laws of classical physical systems, including nonlinear systems.

Interestingly enough though, there is still often great confusion and debate over whether some relatively simple systems can be modelled by Lagrangians.
Special Post: Noether’s First Theorem – Emmy Noether for Ada Lovelace Day

And just by looking at the behavior of this pendulum through a camera, it was able to generate Hamiltonians and Lagrangians mathematical equations that exactly explicate its behavior, something that would probably take someone with a major in physics to write down.

As for QM, well as far as I am aware all QM theories in the standard model are based on Lagrangians or Hamiltonians just as classical models usually are.
Everything You Ever Wanted to Know About Quantum Mechanics, But Were Afraid to Ask

This relationship between fields in this manner involves some subtle matters of Lagrangians on a full space and the ChernSimons Lagrangian on a subchain or cycle.

Since bivectors give you Lie algebras, you get gaugegrouptype things, and you might think of spinors as fermions, and think of the vector space as spacetime, and even try to put such things together to form Lagrangians … and see where Einsteintype faith might lead.

Topics covered include: motivations for supersymmetry, the construction of supersymmetric Lagrangians, supersymmetrybreaking interactions, the Minimal Supersymmetric Standard Model (MSSM), Rparity and its consequences, the origins of supersymmetry breaking, the mass spectrum of the MSSM, decays of supersymmetric particles, experimental signals for supersymmetry, and some extensions of the minimal framework.

Conventional physics uses quadratic Lagrangians, twodimensional worldsheets, secondrank tensors under YangMills groups, commutators between two objects, and similar structures based on the number "2" all the time.

The easiest way to model this system is using Lagrangians/Hamiltonians.

Without any prior knowledge about physics, kinematics, or geometry, the algorithm discovered Hamiltonians, Lagrangians, and other laws of geometric and momentum conservation.
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