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L=T+w? (Lagrangian dynamics)

  1. Mar 27, 2009 #1
    while facing dissipation systems, some books define the L with L=T+w.
    is it universal?
    where is its limits?
    THX!
     
  2. jcsd
  3. Mar 27, 2009 #2

    Ben Niehoff

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    How is w defined? I've never seen it written this way.
     
  4. Mar 27, 2009 #3
    w is the work done on the dynamical system, on matter whether it is dissipative or not.
     
  5. Mar 28, 2009 #4

    Ben Niehoff

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    So, can you give an example of an expression for w, when there is dissipation?
     
  6. Mar 28, 2009 #5
    I've never seen it written in finite form like that, but I would expect that w to represent the work done on the system.

    Hamilton's Principle can be written as
    int(variation of (T*) + variation(W))dt = 0
    where that W is the work of the several forces acting on the system. This is the way that nonconservative forces are included into the formulation of the system equations of motion.
     
  7. Mar 28, 2009 #6
    i got it!

    thanks Ben Niehoff and Dr.D.
     
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