Find the Lagrangian of a simple pendulum of mass m whose point of support moves uniformly on a vertical circle with constant angular velocity.
(So basically there is a circle around the origin that spins with a constant angular velocity and the pendulum is attached to the end of the circle.)
The Attempt at a Solution
I am stuck right in the beginning in trying to find the kinetic energy T. I know that the kinetic energy of a pendulum is..
But since r remains constant on the pendulum because it is rigid, the equation reduces to..
I am unsure how to add the rotating circle in which the pendulum is a attached to. If the problem stated that there was a mass where the pendulum was attached to, it would be easier I think. Should I view this circle as mass-less? How would I get the kinetic energy then? Can anyone provide some help?? :(??