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Math Help - Hamiltonian System

  1. #1
    Len
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    Hamiltonian System

    Consider a system of the form:

    dx/dt=F(y)

    dy/dt=G(x)

    That is, dx/dt depends only on y and dy/dt depends only on x.

    What is the Hamiltonian function?
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  2. #2
    Member Ruun's Avatar
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    Compute the lagrangian L and then

    H = \sum^{i} p_{i}q_{i} - L

    where p_{i} = \frac{\partial L}{\dot{q_{i}}} are the canonical momenta conjugated to the q_{i} coordinates and \dot{q_{i}} = \frac{d}{dt}q_{i}
    Last edited by Ruun; March 28th 2010 at 11:34 AM. Reason: typo
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  3. #3
    Member Ruun's Avatar
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    Do you know the physical interpretation of the Hamiltonian? We are talking about classical mechanics I guess
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