Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook