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ksoileau
Posts:
85
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



