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!

Finding the functional extremum

Tags:
  1. Dec 20, 2014 #1
    1. The problem statement, all variables and given/known data
    I have been given a functional
    $$S[x(t)]= \int_0^T \Big[ \Big(\frac {dx(t)}{dt}\Big)^{2} + x^{2}(t)\Big] dt$$
    I need a curve satisfying x(o)=0 and x(T)=1,
    which makes S[x(t)] an extremum

    2. Relevant equations

    Now I know about action being
    $$S[x(t)]= \int_t^{t'} L(\dot x, x) dt$$
    and in this equation $$ L= \Big(\frac {dx(t)}{dt}\Big)^{2} + x^{2}(t)$$
    3. The attempt at a solution
    Is there any other way I can express Lagrangian to fit in this equation and hence I can do the integral? and is there any general solution for the lagrangian?
     
  2. jcsd
  3. Dec 20, 2014 #2

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Why do you want to do the integral? What is wrong with using the Euler-Lagrange equations? This will give you a differential equation that your solution must satisfy to be an extremum the functional.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Finding the functional extremum
Loading...