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Euler Langrange and Hamiltonian help? watch

1. 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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2. (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:

3. (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:

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) ?
4. (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) ?

2. Yes, you have to do it separately - the label means 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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