Lagrangian Dynamics

Lagrangian Dynamics.

A circle of radius R, oriented with the plane of the circle horizontal, is attached to a vertical axis at one point on the circumference of the circle. A bead, of mass m, is attached to the circle and is free to move around the circle, with no frictional losses.

The circle - bead system rotates about the axis at a constant angular speed of W; in the abscence of any external forces (no gravity) show that the "beads" motion about a point on the circle opposite the point of attachment to the axis is the same as a plane pendulum.

Use Lagrangeian dynamics to model the system.

(Note: response is a hand-written jpg file)