1
$\begingroup$

So if $f(t)=(x(t),y(t))$ with $f(0)=a$ and $f(1)=b$, I should minimize $L(f)=\int_0^1{|\dot{f(t)}|}dt$. I get a jumble of equations when solving the Euler Lagrange equations with respect to $t$. Would someone help explicitly solving them. Please avoid using $y'(x)$ since I am trying to generalize this to n space

Thanks in advanced for any help.

$\endgroup$
0
$\begingroup$

Hint: Consider the squared Lagrangian cf. e.g. this Math.SE post. The shortest curve between $a$ and $b$ is unsurprisingly a straight line.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.