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ksoileau
Posts:
74
From:
Houston, TX
Registered:
3/9/08
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Calculus of Variations question
Posted:
Feb 29, 2012 3:00 PM
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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
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