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The Hamiltonian for a particle moving vertically in a uniform gravitational field \(g\) is \[H=\frac{p^2}{2m} + mgq\]
- Find the new Hamiltonian for new canonical variables \(Q,P\) given by \[ Q=-p, P=q+Ap^2\] Show that we can eliminate \(Q\) from the Hamiltonian (make \(Q\) cyclic) by choosing a constant \(A\) appropriately.
- With this choice of \(A\) write down and solve Hamilton's equations for the new canonical variables, and then use the transformation equations to find the original variables \(q,p\) as functions of time.
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4727:Diamond Point
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