Thanks that was useful. After a quick search, I found this link:
http://www.astro.uwo.ca/~houde/courses/PDF%20files/physics350/Lagrange.pdf
Equation 4.37 is very close to what I need. I also need to account for friction at the hinge. How do I incorporate a constant frictional force?
Also...
What mass is required to keep the seat of a ferris wheel from swinging no more than 30 degrees measured from the vertical axis?
So let's say we have a big ferris wheel with radius R and its spinning at 10 RPM. At the end of the ferris wheel, is a hinge, and a hanging bucket (like the picture)...