Date: Jun 8, 2012 8:32 PM
Author: mbalover9@gmail.com
Subject: What is Euler-Lagrange equation for this form?

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 Euler-Lagrange 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 Euler-Lagrange 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 E-L
equation for this integral.

Thank you.