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Interpretation of the Lagrangian

  1. Nov 21, 2006 #1
    I have showed that if the integrand [tex]f[/tex] in the variational problem
    [tex]\delta (\int f dx ) = 0[/tex]
    does not depend explicitly on the independent variable x, i.e. satisfies [tex]f = f(y, \dot{y})[/tex], then the Euler equation can be integrated to

    [tex]\dot{y} \frac{\partial f}{\partial \dot{y}} - f = const.[/tex]

    How can I give an interpretation of this constant for the case that [tex] f = L[/tex] is the Lagrangian and [tex]x = t[/tex] is the time?
     
  2. jcsd
  3. Nov 21, 2006 #2

    dextercioby

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    It's the energy of the system.

    Daniel.
     
  4. Nov 21, 2006 #3
    So I can interpret this as that the Energy of the system is constant?
     
  5. Nov 21, 2006 #4

    dextercioby

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    Yes, of course. It's a symmetry of the action.

    Daniel.
     
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