Is the LaGrangian tautological?

oldphysicist

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?

DaleSpam

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.

voko

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.