What are some interesting calculus of variation problems? [closed]

That I could create as a classical mechanics class project? Other than the classical examples that we see in textbooks (catenary, brachistochrone, Fermat, etc..)

Answer

Here is one I just made up, but it has a nice flavor— suppose you have a 2-d bullet going very fast through a 2-d gas. The gas molecules reflects specularly off the bullet, making glancing collisions. What shape of bullet of a fixed area has the least drag?

This problem gives

11+y2+λydx

And the equation for y’ you get is

y=λx(12y2y4)

or

y=λx(12y2y4)

Which you can solve in a series by plugging in y=λx22 and iterating a few times using the relation above as a recursion.

Attribution
Source : Link , Question Author : Community , Answer Author :
Ron Maimon

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