# Lagrangian for simple pendulum

by Reshma
Tags: lagrangian, pendulum, simple
 P: 777 Find the Lagrangian for a simple pendulum of mass m whose point of support moves uniformly on a vertical circle with constant frequency $\omega$ in a uniform gravitational field. Let 'l' be the length of the pendulum string. Using plane polar coordinates: Let T be the KE of the pendulum. $$T = {1\over 2}m \left(\dot {r}^2 + r^2\dot{\theta}^2\right)$$ Let V be the PE. $$V = -mgr\cos \theta$$ r = l = constant I am wondering how to add the angular velocity $\omega$ to the equation of motion. Need help here.
 Quote by Reshma Find the Lagrangian for a simple pendulum of mass m whose point of support moves uniformly on a vertical circle with constant frequency $\omega$ in a uniform gravitational field. Let 'l' be the length of the pendulum string. Using plane polar coordinates: Let T be the KE of the pendulum. $$T = {1\over 2}m \left(\dot {r}^2 + r^2\dot{\theta}^2\right)$$ Let V be the PE. $$V = -mgr\cos \theta$$ r = l = constant I am wondering how to add the angular velocity $\omega$ to the equation of motion. Need help here.