Definition:Conjugate Point (Calculus of Variations)/wrt original Functional

Definition
Let:


 * $\displaystyle \int_a^b \map F {x, y, y'}$

be the original functional.

Let $\tilde a$ be conjugate to $a$.

Let:
 * $\displaystyle \int_a^b \paren {P h'^2 + Q h^2} \rd x$

be the second variation of $\displaystyle \int_a^b \map F {x, y, y'}$.

Then $\tilde a$ is conjugate to $a$ to the original functional $\displaystyle \int_a^b \map F {x, y, y'}$.