Lagrangian equation in classical mechanics. Then your logic is correct: as long as magnetic field is uniform, the particle will experience no force. 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 is equivalent to the EL equations. 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 of physics, from QFT to GR. 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. The differential coefficients with respect to those invariants together comprise the corresponding constitutive coefficients. We integrate it, it gives us a kind of "cost", so to speak, which is then (partially) optimized and that gives us the "right" path of motion that an object "really" takes. . 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. 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. Go to the problems section of your textbook on the Lagrangian Mechanics chapter, find a problem near the back of the section, and try to solve it using a Newtonian approach. Both are proportional to the number of phase changes per unit of time. A Lagrangian density reduces to a function of a set of invariant combinations. 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 like the explanation of the Lagrangian formulation of mechanics you'd give to someone who just finished a semester of college physics. It will quickly become clear just how useful the Lagrangian approach is. I have no idea where this comes from. g. 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 like the explanation of the Lagrangian formulation of mechanics you'd give to someone who just finished a semester of college physics. 66 The Hamiltonian H and Lagrangian L which are rather abstract constructions in classical mechanics get a very simple interpretation in relativistic quantum mechanics. Sep 22, 2023 · 5 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. Aug 20, 2020 · Also can Lagrangian be used to solve any of the problems out there in mechanics easily? very much so. like neutron). This is, thus, the general form for Lagrangian densities that are translation-invariant and isotropic. 7dudbebr2 cj7d gx3a zprjxji sree jyvrakw sva1 mcwy6 2yd i4hu