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| As a third example, we consider a pendulum of mass \(m\) and length \(b\) attached to the edge of a disk of radius \(a\) rotating in the vertical plane with angular velocity \(\omega\) in a constant gravitational field with acceleration \(g\). Choose the origin at the center of the disk and \(\theta\) as generalized coordinate, find the Cartesian coordinates of the pendulum mass in terms of \(\omega, a, b\) and generalized \(\theta\). Set up the Lagrangian and the obtain the equations of motion. |  |
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