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Topic: Calculus of Variations question
Replies: 0

 ksoileau Posts: 83 From: Houston, TX Registered: 3/9/08
Calculus of Variations question
Posted: Feb 29, 2012 3:00 PM

Given a function f of two variables x and y, how does one find
functions x(s) and y(s) over the interval [0,1] which locally
extremize the functional \int_0^1{f(x(s),y(s))ds}, where x(s) and y(s)
are constrained by the conditions x(0)=x_0, y(0)=y_0, and
\sqrt(x'(s)^2+y'(s)^2)=1 ?
To put it less formally, how does one find the curve of length 1, with
a fixed initial point, which maximizes or minimizes the functional
\int_0^1{f(x(s),y(s))ds}, where the curve (x(s),y(s)) is parameterized
according to arc length?
Thanks for any feedback.

Standard disclaimer, I'm not a student, this isn't homework. :)

Kerry Soileau