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  1. bananabandana

    Euler Lagrange Derivation (Taylor Series)

    Yes, I know, but why are we allowed to treat ##y(x)## and ##\dot{y}(x)## as independent variables? (as we are required to do for the Taylor series?) They clearly aren't independent.
  2. bananabandana

    Euler Lagrange Derivation (Taylor Series)

    Mod note: Moved from Homework section 1. Homework Statement Understand most of the derivation of the E-L just fine, but am confused about the fact that we can somehow Taylor expand ##L## in this way: $$ L\bigg[ y+\alpha\eta(x),y'+\alpha \eta^{'}(x),x\bigg] = L \bigg[ y, y',x\bigg] +...
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