Re: [Phys-l] Landau on Lagrangian

[Stefan Jeglinski <jeglin@4pi.com>]

> 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