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P.S.
Does EOM mean "energy of motion"?
David wrote:
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.
This does not seem to exclude a linear function of v (ex., L=mv).
Or do I misread your argument?
P.S.
Does EOM mean "energy of motion"?
Bob Sciamanda