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Second variation

  1. Dec 14, 2006 #1
    Let be a functional S so [tex] \delta S =0 [/tex] give the Euler-Lagrange equation where:

    [tex] S= \int_{a}^{b}dtL(q,\dot q, t) [/tex]

    My question is ..How the "second variation" [tex] \delta ( \delta S )=0= \delta ^{2} S [/tex] defined??.. in order we could decide if a function q=q(t) is either a maximum or a minimum point of function space..:confused: :confused: thanks.
  2. jcsd
  3. Dec 15, 2006 #2


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    How's the "first variation" defined ?

  4. Dec 16, 2006 #3
    The first variation of S (are you physicist..i say so because i use to see you in the QM forum :tongue2: ) are the Euler-Lagrange equation defined via the functional derivative
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