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Re: [Phys-l] Landau on Lagrangian

Stefan Jeglinski wrote:
> Why not :
> Ergo: L=L( | v | ) ?


No generality is lost here. Note that |v| is a function of v^2. In particular |v| = sqrt(v^2). So any real function of |v| is also a real function of v^2 as well (because a function of a function is a function).

OK, but the spirit of the question survives, unless I misunderstand you. In the "first principles" approach that's been discussed in this thread, the argument does not appear to preclude one from supposing the free classical particle Lagrangian to be (1/2)m|v|. This would seem justified (Occam's Razor?), other than the rather glaring inability to get N2, which takes us back ultimately to the only argument left: "in our universe, this apparently just doesn't seem to be the case."

Stefan Jeglinski
Interesting topic. One can suppose that the experiment to support the idea that energy of [downwards] translation is proportional to distance is very accessible.
One can suppose that it is also reasonable to suppose that such a movement is accelerating.
But if so, it would be hard to support the proposition that the energy gained
is proportional to both distance and velocity.

Brian W