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| Consider a bead of mass \(m\) sliding freely on a hoop of radius \(R\), rotating in the vertical plane about its vertical diameter, with angular velocity \(\omega\) in a constant gravitational field with acceleration \(g\). Derive and expression for Hamiltonian. Remember the answer for Hamiltonian must always be written as a function of generalized coordinates and canonical momenta. {Hint:} Since the bead of the rotating hoop moves on the surface of a sphere of radius \(R\), use the generalized coordinates given by the two angles \(\theta\) (measured from the negative \(z\)-axis) and \(\phi\) (measured from the positive x-axis), where \(\dot{\phi}=\Omega\). |
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4727:Diamond Point
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