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Question: How would a springy brachistochrone behave?

Question:How would a springy brachistochrone behave?

Earl 955 Maple 2016
differential-equations mechanics brachistochrone
January 23 2020
0

Imagine a brachistochrone shaped path made of a frictionless flexible metal strip which reacts to the force of a weighty sliding object.

Depending on its flexibility and the object's mass, what would be the strip's initial shape for fastest descent between its top and bottom? How would its shape change during the object's descent?

Perhaps an aircraft emergency escape slide or the fastest path for a slalom skier exemplify this kind of situation.
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