66 The Hamiltonian H and Lagrangian L which are rather abstract constructions in classical mechanics get a very simple interpretation in relativistic quantum mechanics. Both are …

78 What is Lagrangian mechanics, and what's the difference compared to Newtonian mechanics? I'm a mathematician/computer scientist, not a physicist, so I'm kind of looking for something …

This is, thus, the general form for Lagrangian densities that are translation-invariant and isotropic. A Lagrangian density reduces to a function of a set of invariant combinations. The differential …

Dec 6, 2013 · The Lagrangian, Hamiltonian formalism (with the min action principle ) represent a minimal mathematical framework that can explain a lot of experimental data, from all domains …

The point was, I wanted to have a physical interpretation of the Lagrangian, and leave the action and the principle as abstract constructions done for who knows what reason, probably …

Oct 12, 2020 · Lagrangian mechanics uses the energy equation (1) to find the trajectory with the property that the rate of change of kinetic energy matches the rate of change of potential energy.

May 19, 2024 · I understand this sentence in the following way. We want the (coordinate representative) of the Lagrangian with respect to the primed coordinates to be equal to the …

And the Lagrangian is the answer to that, although it's not a 100% satisfactory one because the path that is taken need not strictly speaking be the truly least action path. We integrate it, it …

Apr 11, 2021 · In the context of translation symmetry for lagrangian mechanics i was given this statement: For a mechanical system $\frac {∂L} {∂\dot {q}_i}=p_i$ is the momentum. I have no …

Sep 22, 2023 · As was said in the commentary by @knzhou, what you have written is the Lagrangian for a particle with magnetic moment and no charge (e.g. like neutron). Then your …