Definition:Conjugate Point/wrt original Functional
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What exactly is meant by "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 $\displaystyle \int_a^b \map F {x, y, y'}$.
What exactly is meant by "original functional"?
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