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What is EulerLagrange equation for this form?
Posted:
Jun 8, 2012 8:32 PM


Hi all,
I am not a math student. I am a software engineer and I am trying to program an algorithm which tries to solve an optimization problem. So please do not think this is a question about homework.
I already looked at many Calculus of Variations textbooks and only find the EulerLagrange equations for this form: E = Integral f(x,y,x',y',s)ds where x and y are functions of the independent variable s. x', y' are 1st derivatives of x and y. E is the cost function to minimize.
However my cost function has the form
E = Integral f(x,y,x',y', x'', y'' ,s)ds. where x'' and y'' are 2nd dertivatives
Could you please let me know what are the EulerLagrange equations for my cost function? Or please point me a book that helps to derive the E L equation of my form? Or at least some hints how to derive the EL equation for this integral.
Thank you.



