1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Variational methods conjugate points

  1. Mar 3, 2008 #1
    (a will be alpha and b will be beta)
    Let y=y(x,a,b) be a general solution of Euler's equation, depending on two parameters a and b. Prove that if the ratio (subdifferential y/subdifferential a)/(subdifferential y/subdifferential b) is the same at the points, the points are conjugate.

    I cannot find the theorem to use for this. i am suppose to take the derivative with respect to a and b and find the ratio. but i am looking for that something to take the derivative of.

    As well, the definition of conjugate points is as follow:
    The point a tilda (does not equal a) is said to be conjugate to the point a if the equation -d/dx(Ph')+Qh = 0 has a solution which vanishes for x=a and x=a tilda, but is not identically 0.

    I have been looking over and over on the internet for this, I cannot show any work as I really do not know how to do it without the proper theorem.
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?



Similar Discussions: Variational methods conjugate points
  1. Revised Simplex Method (Replies: 0)

  2. Numerical methods (Replies: 0)

  3. Using Heuns method (Replies: 0)

  4. Equilibrium points (Replies: 0)

Loading...