Extremal paths
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Consider the action for a particle in a potential U.
a. Show that an extremal path is never that of a local maximum for the action. ("Local" means relative to nearby paths).
b. Find an example in which an extremal path is that of a local minimum for the action.
c. Find an example in which an extremal path is not that of a local minimum for the action.
https://brainmass.com/physics/scalar-and-vector-operations/extremal-paths-32862
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