Lagrangian for Flywheel System:

Find the Lagrangian for the system shown in the figure below. The particle $m_2$ moves on a vertical axis and the whole system rotates about this axis with a constant angular velocity $\Omega$.

From the Lagrangian, find the equations of motion. That is a pretty disgusting differential equation to solve, as far as I can see. Do you know any tricks?

Following the ``Hamiltonian-recipe'', find the Hamiltonian and the equations of motion. The $\dot{\theta}$ equation isn't to bad, but $p_{\theta}$ isn't so pretty.