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Calculus of variations with isoparametric constraint

  1. Jun 10, 2014 #1
    We seek stationary solutions to
    [itex]\int_{x_0}^{x_1} F(x, y, y')dx[/itex]
    subject to the constraint
    [itex]\int_{x_0}^{x_1} G(x, y, y')dx = c[/itex]
    where [itex]c[/itex] is some constant.

    I have read that this can be solved by applying the Euler Lagrange equations to
    [itex]F(x, y, y') + \lambda G(x, y, y') [/itex]
    and then finding the appropriate value of [itex] \lambda[/itex] when solving so that the constraint is satisfied.

    Why does this work? I am not sure what reference to use.

    Also, this may still work when the unconstrained integral has no stationary solutions, right?
     
  2. jcsd
  3. Jul 2, 2014 #2
    I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?
     
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