# 'Floating' Disc on an Inverted Pendulum

1. Nov 19, 2008

### shieldsy29

1. The problem statement, all variables and given/known data
A cylinderical rod of length (l), and diameter (d) and evenly distributed mass (m) is oscillating harmonically (ie y(t) = Acos(wt)) with a driven frequency that makes the rod stable in the upright postion (ie inverted pendulum)
A ring/disc of mass m' is fitted over the rod with small clearance. The rod is then tilted at a small angle from the y-axis and oscillated with a driving frequency until the disc remains in a stable position - 'floating' on the rod.

2. Relevant equations

3. The attempt at a solution

Really what I've described above is hopefully what will happen at the end of my project this year!
I've been able to derive the equation of motion for an inverted pendulum (rod), but I'm struggling now with how to proceed when the disc/ring is added to the problem.
What i need to find out is if the stability of the disc is dependent on the friction between the disc and the rod, or if a slight bending moment needs to be applied to the rod for the ring to remain stable. Or a combination of both.
Does anyone know how i should proceed with the problem? Of course I realise this may be a problem that is hard to solve over the internet but any help would be appreciated.