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I wrote: . . .
But even If I grant you these requirements and accept that they
imply that the mechanical L = L(v^2), you still have to show that
this implies: KE(translation) is proportional to v^2.
To which David Bowman responded:
That was already done (more than once). That comes from the
invariance of the EOM under Galilean boosts once it is granted
that the resulting equations be no higher than 2nd order and
the symmetries of space & time homogeneity and spatial isotropy
are imposed. Please reread the part of the argument about how
only the expression v^2 obeys v^2 = v'^2 + dF/dt when
v = v' + v_0 and F = F(r',v',t). Other nonlinear functions of
v^2 do not have this property.
Those arguments only attempt to show that L = L(v^2).
They do not address the proposition: KE(translation) is
proportional to v^2.
How does the concept of KE even enter the development?
Bob Sciamanda