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Landau Lifshitz - Total time derivative of the Lagrangian

  1. Jul 24, 2012 #1
    On page 13 in Landau-Lifgarbagez Mechanics, the total time time derivative of the Lagrangian of a closed system is given to be,

    [tex]\frac{d L}{d t} = \sum_i \frac{\partial L}{\partial q_i} \dot{q_i} + \sum_i \frac{\partial L}{\partial \dot{q_i}} \ddot{q_i}[/tex]

    Why does this stop here? I mean, why is the term [itex]\sum_i \frac{\partial L}{\partial \ddot{q_i}} \dddot{q_i}[/itex] not included?

    An image of page 13 has been attached.

    Attached Files:

    Last edited: Jul 24, 2012
  2. jcsd
  3. Jul 24, 2012 #2
    Because in classical mechanics the lagrangian is a function only of generalized coordinates and velocities. Read section 1 and 2 of the same book.
  4. Jul 24, 2012 #3
    Thanks for the reply Dickfore. You are correct.
  5. Jul 24, 2012 #4
    It is a function of t only if the system is open.
  6. Jul 24, 2012 #5
    Thanks. Again you are correct.
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