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Old Feb 5th 2019, 09:10 PM   #1
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Trying to get my head around the Lagrangian

In the calculus of variation they set up the problem as action S



where and

In the case of finding the shortest distance between two points this makes sense but in the case of finding the path of least time as in a roller coaster shaped like a e Brachistochrone
I am not getting why the case of applies?

How does this work in that case?
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Old Feb 5th 2019, 10:34 PM   #2
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ok, I misread the Brachistochrone problem. it also involves two points and finding a path between them.
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