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Euler Lagrange method, just not getting it at all

  1. Sep 18, 2011 #1
    1. The problem statement, all variables and given/known data

    In Classical mechanics 2 i have an assignment based on the Euler Lagrange method and i cannot seem to grasp the concept, even with all the internet resources i can find as well as my two textbooks which have a chapter on it. (Boass (Mathematical methods in teh physical science) and Taylor Classical Mechanics) The first have of the assignment he has given us is two questions which he has made up as well as 3 from Taylor

    2. Relevant equations

    [itex]\frac{\partialF}{\partialy} - \frac{d}{dx}\frac{\partialF}{\partialy'}[/itex]


    3. The attempt at a solution

    The Boass textbook seems to have more straight math based questions, which i have been trying to practice with, and for some reason i am having no luck even with these


    chapter 8 section 2 of boass

    1. [itex]\int \sqrt{x}\sqrt{1+y'^{2}}[/itex]

    using the equation above [itex]\frac{\partialF}{\partialy}[/itex] = 0

    So then [itex]\frac{d}{dx}\frac{\partialF}{\partialy'}[/itex] = 0

    So [itex]\frac{\partialF}{\partialy'}[/itex] = constant = [itex]\frac{\sqrt{x}y'}{\sqrt{1 + y'^{2}}}[/itex]

    shuffling it around i would get

    y' = [itex]\frac{c^{2}}{c^{2} - x^{2}}[/itex]

    integrate with respect to x

    i think is arcsin (x/c)

    Not sure if this is right because there is no answer in the back

    One that does have an answer in the back i get no where near close to

    6. [itex]\int( y'^{2}[/itex] + [itex]\sqrt{y})[/itex]dx

    if i use the euler lagrange

    [itex]\frac{\partial F}{\partial y}[/itex] = [itex]\frac{1}{\sqrt{4y}}[/itex] which does not equal 0

    so [itex]\frac{d}{dx}\frac{\partial F}{\partial y'} \neq 0[/itex]

    and now this is where i have no idea what to do

    the answer to the question is

    x + a = (4/3)(y1/2 -2b)(b + y1/2)1/2

    any help will be much appreciated
     
  2. jcsd
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