Question regarding generalized momentum Pk, and its independence from gen. coord. Qk

1. Aug 16, 2012

sempiris

Hi Physicsforums

I am re-learning classical mechanics and having a tough time dealing with a certain line from Thornton/Marion. On page 269 (5th ed), a little after introducing Hamiltonian dynamics and the canonical conjugate equations of motion, the author says: "the qk and the pk are independent, whereas the qk and the $\dot{q}$k are not". The context is describing the advantages of using Hamiltonian dynamics over Lagrangian

In my mind, I see pk = m$\dot{q}$k. If this is the case, I don't see how the author's statement stands.