Is the LaGrangian tautological?

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The discussion centers on the potential tautology of the Lagrangian formulation in classical mechanics, specifically the expression L = T - V, where L represents the Lagrangian, T is kinetic energy, and V is potential energy. The participant argues that deriving equations of motion from the Lagrangian requires prior knowledge of T and V, creating a circular reasoning issue. Furthermore, they assert that in field theory, identifying T and V is empirical rather than tautological, as the choice of Lagrangian is based on its ability to produce equations of motion that align with empirical observations.

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oldphysicist
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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?
 
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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.
 
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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