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Isoperimetric problem

  1. Jan 13, 2012 #1
    1. The problem statement, all variables and given/known data
    The isoperimetric problem is of the finding the object that has the largest area with the equal amount of perimeters; however, how does the integral constrained by the arc length get maximized? http://mathworld.wolfram.com/IsoperimetricProblem.html


    2. Relevant equations



    3. The attempt at a solution
    ...finding a point at which the integral is like finding the max and min of a function of two variables...
     
  2. jcsd
  3. Jan 13, 2012 #2

    LCKurtz

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    The general subject is Calculus of Variations. One place to read about it is here:

    http://www.google.com/url?sa=t&rct=...sg=AFQjCNGZoq3YfZweM8ZFKBWuB062RSvkZQ&cad=rja
     
  4. Jan 13, 2012 #3
    It says the shortest path is the straight line; however, the brachistochrone problem proves that it is actually a curved line on which a stone could accelerate more. OK, brachistochrone problem is discussed. But why is on page 1163, the Euler Lagrangian equal to [tex] -\frac{u"}{(1+(u')^2)^{\frac{3}{2}}}[/tex]? I got -u"+(u')^{2}u" for numerator.
     
    Last edited: Jan 13, 2012
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