What is the difference between Newtonian and Lagrangian mechanics …
Lagrangian mechanics are better when there are lots of constraints. The more the constraints, the simpler the Lagrangian equations, but the more complex the Newtonian become. Lagrangian …
What is the physical meaning of the action in Lagrangian mechanics?
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 proportional to the number of …
Physical meaning of the Lagrangian function [duplicate]
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 because the principle …
The origin of the Lagrangian - Physics Stack Exchange
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.
Deriving Lagrangian density for electromagnetic field
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 …
Derivation of Maxwell's equations using Lagrangian formalism
Mar 4, 2024 · The use of the Lagrangian formalism is not restricted to (point) mechanics, but all fundamental interactions (electroweak, strong, gravitation) are defined by the action integral of a …
On Landaus&Lifshitz's derivation of the lagrangian of a free particle ...
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 (coordinate …
Momentum in Lagrangian mechanics - Physics Stack Exchange
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 idea …
How does the Lagrangian work with a magnetic field?
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 logic is correct: as long …
Connection between different kinds of "Lagrangian"
Mar 21, 2021 · The third definition is different. Of course it is also related in the sense that in Lagrangian formulations of dynamics or variational problems, Lagrange multiplier methods often appear. But this …