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

How to get the Lagrangian that generates certain diff equation ?

  1. Sep 14, 2008 #1
    how to get the Lagrangian that generates certain diff equation ???

    I have an ordinary differential equation of second order. I am looking for the Lagrangian(s) for which this equation is the Euler-Lagrange equation. I need a practical reference specifically written for one degree of freedom (one equation), I'm not interested in general theorems of existence or highly geometrical language. I found some reference by Darboux in 1894 but its in French. Any english reference?
     
    Last edited: Sep 14, 2008
  2. jcsd
  3. Sep 18, 2008 #2
    Re: how to get the Lagrangian that generates certain diff equation ???

    Got it. The problem is known as 'inverse problem of variational calculus'. For future references:

    N. Akhiezer, "The Calculus of Variations", 1962:

    page 166: example of 1D problem

    R. Santilli, "Foundations of Theoretical Mechanics II", Springer-Verlag, 1983:

    page 353: reworking the same example as Akhiezer
    page 315: by knowing one first integral, Kobussen's method

    R. Santilli, "Foundations of Theoretical Mechanics I", Springer-Verlag, 1978:

    page 201: Douglas approach for n-dimension, easily applied to n=1
    page 208: first obtaining Hamiltonian and then get the Lagrangian through inverse Legendre transformation
     
    Last edited: Sep 18, 2008
  4. Sep 18, 2008 #3

    atyy

    User Avatar
    Science Advisor

    Re: how to get the Lagrangian that generates certain diff equation ???

    Thanks for the pointers!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: How to get the Lagrangian that generates certain diff equation ?
  1. Lagrangian Equation (Replies: 1)

Loading...