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Interesting Calc of Variations Problems

  1. Aug 25, 2011 #1
    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.
  2. jcsd
  3. Aug 26, 2011 #2


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    Homework Helper

    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.
  4. Nov 9, 2011 #3
    you should try ramsey's model its an aplication to economics
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