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Is the LaGrangian tautological?

  1. Aug 4, 2012 #1
    This issue has always bothered me, and I would like to hear a logical resolution. The classical prescription for finding it is L=T-V. From the LaGrangian, the equations are motion are then deduced using the Euler-LaGrange eqs. But - the equations are motion are required in order to determine T and V, since they (eqs. of motion) are necessary to determine the forces, which will be used to calculate T and V. So it looks like a big circle to me ????????

    Also, when applied to field theory (classical or quantized) how do you identify T and V, if you want to use the basic definition L=T-V?
  2. jcsd
  3. Aug 4, 2012 #2


    Staff: Mentor

    I would say it is empirical rather than tautological. You use a given Lagrangian because it gives equations of motion that match what is observed empirically.
  4. Aug 4, 2012 #3
    No, forces are not used in the "pure" Lagrangian formulation. Kinetic energies are obtained directly via [itex]T= \frac {m v^2} {2}[/itex] in whatever coordinate systems employed, potential energies are considered given empirically.
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