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    I'm trying to use the Euler Lagrange and Hamiltonian on the Kepler problem. I managed to use the E-L equations correctly but I'm having trouble with the Hamiltonian where there is a * on the attachment. I'm supposed to get L (top of page) but I get some extra terms that underlined and I don't know what I'm doing wrong????
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    (Original post by e^x)
    I'm trying to use the Euler Lagrange and Hamiltonian on the Kepler problem. I managed to use the E-L equations correctly but I'm having trouble with the Hamiltonian where there is a * on the attachment. I'm supposed to get L (top of page) but I get some extra terms that underlined and I don't know what I'm doing wrong????
    As far as I can see (picture too small), you don't seem to be computing the generalised momenta correctly. These are:

    p_i = \frac{\partial L}{\partial \dot{q}_i}

    i.e. p_r = \frac{\partial L}{\partial \dot{r}} = m \dot{r} using your Lagrangian.
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    (Original post by atsruser)
    As far as I can see (picture too small), you don't seem to be computing the generalised momenta correctly. These are:

    p_i = \frac{\partial L}{\partial \dot{q}_i}

    i.e. p_r = \frac{\partial L}{\partial \dot{r}} = m \dot{r} using your Lagrangian.
    Sorry about the pic. If you can see, on the fourth line I have calculated the momenta
    P = m*r(dot) + m*r^2*theta(dot)
    Is this not correct?

    Or am I suppose to do it separately to get
    P1 = m*r(dot)
    P2 = m*r^2*theta(dot) ?
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    (Original post by e^x)
    Sorry about the pic. If you can see, on the fourth line I have calculated the momenta
    P = m*r(dot) + m*r^2*theta(dot)
    Is this not correct?

    Or am I suppose to do it separately to get
    P1 = m*r(dot)
    P2 = m*r^2*theta(dot) ?
    1. Please use latex

    2. Yes, you have to do it separately - the label p_i means p_r, p_\theta in this case. There is one generalised momentum for each generalised coordinate. A generalised momentum need not have units of linear momentum, BTW.
 
 
 
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