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.