Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.
|
|
Rod
Posts:
521
Registered:
12/7/04
|
|
Re: What is Euler-Lagrange equation for this form?
Posted:
Jun 9, 2012 8:57 AM
|
|
"MBALOVER" <mbalover9@gmail.com> wrote in message
news:7715bb07-7103-4e06-8dfd-cdb20e11b024@x6g2000pbh.googlegroups.com...
> 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.
>
http://en.wikipedia.org/wiki/Euler%E2%80%93Lagrange_equation
under the heading "Single function of two variables with higher derivatives"
|
|
|
|
