Which curve joining the points (0,0) and (1,0) minimizes the integral $$ J[y]=\int_0^1(y'')^2 dx. $$ subject to the condition $$ \int_0^{1} (y')^2dx=1, $$ if $y(0)=0$, $y'(0)=\alpha$ and $y(1)=0$.
minimizing constraint problem
1
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calculus
calculus-of-variations
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0Where are you stuck? What have you tried? Do you know the Euler-Lagrange equation you need to solve? – 2012-11-25