# [SOLVED] transversality condition

• Jan 10th 2010, 02:29 AM
0123
[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
• Jan 13th 2010, 08:59 AM
Rebesques
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.