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June 25th, 2016, 06:57 PM   #1
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Euler Lagrange

I'm looking at the Euler-Lagrange equation derivation,
df/dy-d/dx(df/dy')=0

In the derivation, they treat the the original integral, int(f(y',y,x)dx) like a regular calculus max/min problem, that is, they take the derivative with respect to some 'variance', while keeping the limits of the integral the same, and set it to zero, and from there make their way to the Euler-Lagrange equation... the goal being to find the conditions such that y(x) is the shortest path between two points.

The variance is defined by a new function, Y(x) = y(x) + εg(x), where I take it that ε takes on arbitrary real numbers of multiplied by an arbitrary function g(x).

I don't understand how this all really works and why we can treat the problem like a calculus problem, I don't even know enough to ask the right questions to help me understand it better....

What can I learn that will ultimately help me understand this?

Last edited by skipjack; June 26th, 2016 at 12:53 AM.
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June 26th, 2016, 12:55 AM   #2
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What book or article are you using?
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June 27th, 2016, 12:01 PM   #3
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This wasn't originally what I was looking at, but its the same derivation:

Derivation of the Euler-Lagrange-Equation — Martin Ueding
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