Interesting Calc of Variations Problems

[ehsteve]

Hi everybody,

I'm a long-time reader and new poster. At the moment I am looking for some interesting Calculus of variations problems to present to 2nd year maths students.

Naturally, I am already looking at the historical problems, The Brachistochrone, and I also have an applications of minimal surface area using bubbles.

I had also considered crafting a question out of non-euclidean geometry, which looks at shortest distance over a sphere.

I have also considered the cruise climb problem of minimizing fuel while an aircraft climbs to cruising altitude.

I am looking for a couple more ideas problems that will make students really think, and not just sit there bored out of their brains.

I would give more details, but I have to run to work.

 

[hunt_mat]

I once saw geodesics on the cylinder, given by my old lecturer. The book Analytical Mechanics by Louis N. Hand and Janet D. Finch offers some fun and interesting problems.

 

[aortizmena]

you should try ramsey's model its an aplication to economics