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Question: Can a smooth path of fastest descent be found between two points on a surface?

Question:Can a smooth path of fastest descent be found between two points on a surface?

Earl 980 Maple 2016
surface fastest-descent
October 07 2017
2

The linked worksheet displays the geodesic between two points on a surface z(x,y).

Surfacepath.mw

Gradient descent will find a stepped approximate path of fastest descent between the points, but is there a way to find a function defining an exact i.e. smooth path of fastest descent? If so, how can a precise time of fastest descent be determined?
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