Definition:Conjugate Point/wrt original Functional
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Definition
Let
- $ \displaystyle \int_a^b F \left ( { x, y, y' } \right ) $
be the original functional.
Let $ \tilde a $ be conjugate to $ a $.
Let
- $ \displaystyle \displaystyle \int_a^b \left ( { Ph'^2 + Qh^2 } \right ) \mathrm d x$
be the second variation of $ \displaystyle \int_a^b F \left ( { x, y, y' } \right ) $.
Then $ \tilde a $ is conjugate to $ a $ with respect to to the original functional $ \displaystyle \int_a^b F \left ( { x, y, y' } \right ) $.
