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Time-independence of original coordinates in canonical transform

  1. Dec 12, 2013 #1
    I am going through my professors notes on generating functions. I come across the following equation:

    [tex]\frac{\partial}{\partial t} \frac{\partial F}{\partial \xi^k} = \frac{\partial}{\partial t} \left( \gamma_{il} \frac{\partial \eta^i}{\partial \xi^k}\eta^l - \gamma_{kl}\xi^l \right ).[/tex]

    Here [itex]\xi[/itex] are the original coordinates, [itex]\eta[/itex] are the transformed coordinates, and [itex]\gamma_{il}[/itex] are the components of the block matrix

    [tex]\left( \begin{array}{ccc} 0 & -I \\ 0 & 0 \end{array} \right ).[/tex]

    When the time derivative is taken on the right hand side, the [itex]\xi^l[/itex] are said to be independent of time. Why is this. Certainly (q,p) depend on time, right?
  2. jcsd
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