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I should add that pedagogically, after the WE theorem has
been applied to
a conservative force, one might speculate about a broader energy
conservation possibility. But in mechanics the potential
function is far
from the energy concept of the FLT - the two are connected
only by wild
speculation. The mechanical potential function only enables
one to define
a scalar constant of the motion, and to represent certain
forces as the
gradient of a potential function - it really (of itself)
gives no hint of
the universal FLT - this is rooted in speculation and the
generalization
of experiments (Joule).