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Re: [Phys-l] Landau on Lagrangian

I can't seem to locate my copy of L & L book at the moment. But I thought I remembered that their argument also included (besides Hamilton's Principle, spatial homogeneity, temporal homogeneity, spatial isotropy) the additional requirement that the EOM be invariant under Galilean Transformations so that Galilean relativity holds.

Yes, that is in there too, and was specifically referred to in the reference given later by Curtis O. I had inadvertently omitted it; in fact, I overlooked its importance to the argument that was presented.

<snip details>

If we have any other nonlinear function of v^2 (not proportional to the above linear one or with an affine offset) then substituting v' + v_0 = v into the nonlinear function of v^2 will not result in the same function of v'^2 plus a total time derivative of some function of the dynamical variables, and thus the resulting EOM will not be frame invariant under GTs.

Thanks, this helps me to understand the argument much better...

Stefan Jeglinski