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Second derivative in Lagrangian

  1. Sep 19, 2009 #1
    3. The attempt at a solution
    I have calculated a Lagrangian for a particular system (I can post the problem upon request). The system has two degrees of freedom, but I have applied a constraint to remove one of the degrees of freedom. In doing so, I have introduced a second time-derivative of the position variable. My question is, how does one deal with second derivatives in the Lagrangian formalism?

    The variable and its first derivative are treated as totally independent quantities when solving the Euler-Lagrange equation, so what do I do with a second derivative? Do I treat it as a second derivative of the position variable? Or do I treat it as the first derivative of the derivative? Or do I treat it as a third independent variable? Or do I have to apply the constraint in a way that avoids introducing the second derivative?

    I'm happy to post the question if requested, but I think the question is a pretty basic, general question about the use of the Euler-Lagrange equation that probably doesn't need a specific example. Cheers.
  2. jcsd
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