[QUE/CM-08001]

A mass point $M$ is moving under gravity along a rod, which rotates about the vertical axis passng through the fixed end of the rod. The angle between the rod and the vertical axis remains constant equal to $\alpha$.

1. Set up the Newtonian equations of motion
2. Set up the Lagrangian and obtain the equations of motion.
3. Discuss the motion using the generalized coordinates in (b).

  [SDG]