The 
-variation is a variation in which
the varied path over which an integral is evaluated may end at different times than
the correct path, and there may be variation in the coordinates at the endpoints.
The 
-variation is a variation in which
the varied path in configuration space terminates at the endpoints representing the
system configuration at the same time 
and 
as the correct path; i.e., the varied path always returns to the same endpoints in
configuration space, so
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