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+y′2+λydx

And the equation for y’ you get is

y′=λx(1−2y′2−y′4)

or

y=∫λx(1−2y2−y4)

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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