[tex]

\int_{A}^{B} \sqrt{F\mathbf{(r)}} dr

[/tex]

and

F=a-bz^2 , b>0, a-bd^2>0

the minimum of the action integral is equivalent to

[tex]

\frac{d}{dt}\frac{dG}{\dot{z}}-\frac{dG}{z}=0

[/tex]

where

[tex]

G=\sqrt{F}

[/tex]

or am i doing this in a completeley wrong way?