Consider a bead of mass m constrained to move along a vertical hoop of radius R. The hoop is rotating about a vertical axis through the center of the hoop with constant angular velocity. The gravitational force is acting along the negative z-axis. How many constraints and generalised coordinates are there in the system? Calculate the Lagrange equations of motion and subsequently formulate the Hamiltonian and Hamiltionian equations of motion.

Consider a bead of mass m constrained to move along a vertical hoop of radius R. The hoop is rotating about a vertical axis through the center of the hoop with constant angular velocity. The gravitational force is acting along the negative z-axis. How many constraints and generalised coordinates are there in the system? Calculate the Lagrange equations of motion and subsequently formulate the Hamiltonian and Hamiltionian equations of motion.