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Math Help - [SOLVED] transversality condition

  1. #1
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    [SOLVED] transversality condition

    I need some help with the transversality condition.

    I have a functional to minimize over an admissible class with one free end value
    here it is

    $int x'(1 + t^2*x')dt$

    with $x(1)= 1$

    the Euler equation gives me

    $(1-c)/(2t) + c_1$

    the transversality condition to be satisfied at $t= 2$ is

    $f_x' (2, x(2), x'(2)) = 0$

    can you please show me the steps to get c and $c_1$ using the transversality and the fixed end value?

    thanks for the help
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  2. #2
    Super Member Rebesques's Avatar
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    The minimum is x(t)=-c/t+c_1, \ x\geq 1. The condition x(1)=1 gives one equation involving c and c_1, and the transversality condition 0=f_{x'}(2.x(2),x'(2))=1+2t^2x'(2) gives another.
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