Lagrangian method formula. Mar 21, 2021 · The third definition is different. But this third definition of a Lagrangian gets its name because of Lagrange multipliers, rather than because they are in any ways related to Lagrangians of variational problems. 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. May 2, 2020 · The definition of a symmetry of a theory is quite clear at the level of a Lagrangian. This regards the proof in $\\S 7$ that space homogeneity implies conservatio 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. The Legendre transformation (3) is often referred to as integrating out$^1$ the momentum variables $p_i$. Jul 31, 2024 · In reading the first chapter of Mechanics by Landau and Lifshitz, there is one point on which I consistently get stuck. Nov 9, 2024 · The Lagrangian formulation can get complicated with non-conservative systems and more generally forces that are not obtained by the gradient of a potential - the generalized forces must be added by hand and in these situations the Lagrangian approach is clearly a variation on the Newtonian approach. Is it possible to work with the real Lagrangian density and somehow get the correct commutation relations? I would have expected two Lagrangians differing by total derivative terms to give identical commutation relations (since canonical transformations preserve them). The Lagrangian is one implementation of an underlying geometry, called a "symplectic" geometry that connects kinematic variables with their conjugate dynamic variables, in the description of dynamics and laws of motion. I am not the best person to Nov 9, 2024 · The Lagrangian formulation can get complicated with non-conservative systems and more generally forces that are not obtained by the gradient of a potential - the generalized forces must be added by hand and in these situations the Lagrangian approach is clearly a variation on the Newtonian approach. We say a Lagrangian $\mathcal {L} (\phi,\partial_\mu \phi)$ is symmetric under the transformation $\phi \mapsto \phi + \epsilon \delta \phi_s$ if, when evaluated off-shell, the Lagrangian varies by a total derivative as 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. Jun 21, 2015 · Formula (3) is the succinct answer to OP's question about how to construct the Lagrangian from the Hamiltonian. Of course it is also related in the sense that in Lagrangian formulations of dynamics or variational problems, Lagrange multiplier methods often appear. I am not the best person to .
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