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Interesting calculus of variations problems?

  1. Nov 30, 2011 #1
    Hi, I would like to know if anyone has good ideas for problems involving calculus of variations, other than the classic textbook questions (brachistochrone, Fermat, catenary, etc..) that I could create as a classical mechanics class project? Thank you
  2. jcsd
  3. Nov 30, 2011 #2
    How about verifying that the path of a projectile in a uniform gravitational field really does minimize the action?

    Since we know the path from Newtonian mechanics is a parabola

    y = h - ax2 if x is measured from the peak y=h,

    it would be interesting to pick a one-parameter family of curves, say

    y = h - bnxn

    that has the same endpoints. Then calculate the action (the time integral of kinetic minus potential energy) as a function of n and show that it is minimized for n=2.

  4. Dec 1, 2011 #3
    check the "structure and interpretation of classical mechanics" book (available online)
  5. Dec 1, 2011 #4


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