# Definition:Conjugate Point/wrt original Functional

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## 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 $a$ with respect to to the original functional $\displaystyle \int_a^b \map F {x, y, y'}$.