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Lagrangian equation proof

  1. Oct 15, 2006 #1
    Show that the Lagrange equations of the form
    [tex]{d\over dt}\left(\frac{\partial T}{\partial \dot{q_j}}\right) - \frac{\partial T}{\partial q_j} = Q_j[/tex]
    can also be written as
    [tex]\frac{\partial \dot{T}}{\partial \dot{q_j}} - 2\frac{\partial T}{\partial q_j} = Q_j[/tex]

    Well it can be easily show that:
    [tex]{d\over dt}\left(\frac{\partial T}{\partial q_j \right)} = \frac{\partial \dot{T}}{\partial {q_j}}[/tex]
    Using the operator relation:
    [tex]\frac{d}{dt} \frac{\partial}{\partial x} = \frac{\partial}{\partial x} \frac{d}{dt}[/tex]

    Can this be applied here?
     
    Last edited: Oct 15, 2006
  2. jcsd
  3. Oct 18, 2006 #2
    Come on folks, help me out on this. There's got to be a solution. :frown:
     
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