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Legrende transform of a Lagrangian

  1. Jan 5, 2013 #1

    Uku

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    1. The problem statement, all variables and given/known data

    I am given a Lagrangian, which, per assignment text, describes a single degree of freedom:

    [itex]L= \frac{I}{2}(\dot{q}+\omega)^2-kq^2[/itex]

    I need to find the Hamiltonian.

    Now, what I am wondering, when performing the Legrende transform:

    [itex]H=\sum_{j}p_{j}\dot{q}_{j}-L(q_{j},\dot{q}_{j},t)[/itex]

    Do I concider [itex]\omega[/itex] as velocity, eg. there are two members of the sum: [itex]\sum_{j}p_{j}\dot{q}_{j}[/itex]? The assignment states one degree of freedom.. so I'm a bit insecure on that.

    U.
     
  2. jcsd
  3. Jan 5, 2013 #2

    TSny

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    Homework Helper
    Gold Member

    If there is only one degree of freedom (##q##), then ##\omega## would just be a constant or some parameter. So, only one term ##p\dot q## in the transformation.
     
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