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Lagrangian    
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  • What is the difference between Newtonian and Lagrangian mechanics in a . . .
    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 mechanics is not very suited for non-ideal or non-holonomic systems, such as systems with friction Lagrangian mechanics is also much more extensible
  • 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 phase changes per unit of time The Hamiltonian runs over the time axis (the vertical axis in the drawing) while the Lagrangian runs over the trajectory of the moving particle, the t’-axis
  • 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 is equivalent to the EL equations
  • The origin of the Lagrangian - Physics Stack Exchange
    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
  • newtonian mechanics - Motivation for form $L = T - V$ of Lagrangian . . .
    Summarizing, Lagrangian, Newtonian and Hamiltonian mechanics are different mathematical frameworks whose goal is to describe the same physics The postulates of classical mechanics hold for all formalism, because they are facts of Nature, and we can use them to realize the passage from one to another scheme Of course, one must treat mathematical objects with care in order to gain the equivalence
  • What makes a Lagrangian a Lagrangian? - Physics Stack Exchange
    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
  • Is there a proof from the first principle that the Lagrangian $L = T - V$?
    Lagrangian or Hamiltonian and the derived equations of motion are generalizations and more on the theory side, relatively speaking; at least those are a little more theoretical than Newton's laws We still go to lab to verify these generalizations, but it's somewhat harder to do so, like we have to use Large Hadron Collider
  • Lagrangian of Schrödinger field - Physics Stack Exchange
    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)





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